Hussein Hajji Wario's original post can be located here please read it before you proceed with this response, all rights for the original post belongs to Hussein.
Hussein quotes are in BLUE.
"The Jesus Muslims believe in, the one mentioned in the Qur’an and the Hadith, is not Jesus Christ. Therefore, Muslims do not believe in Jesus Christ. They do not believe in Jesus Christ because Jesus Christ suffered and died on the cross"
This is no more than a re-hash of the old "The Jesus you believe in is not the Jesus we believe in" argument , to a certain degree this is true , Muslims and Christians don't believe in the exact same Jesus down to every detail however both Muslims and Christians believe in the existence of the historical Jesus , each one of our scriptures (the quran and the bible) makes certain claims about Jesus (pbuh) , this does not mean they (the quran and the bible) are not speaking of the exact same historical figure , I will demonstrate what I mean using the following analogy :
"Beth was convicted for murder , the family of the victim believes she is guilty because her finger prints were on the gun but the family of Beth believes she is innocent because Beth was framed by her husband who tricked her into grabbing the gun earlier that day"
In this case , both families are speaking of the same person (Beth) , but each family has its own set of ideas about the figure in question , this does not mean both families are not speaking about the same figure , similarly Muslims and Christians share many details about Jesus (pbuh) but differ on others , so if we want to approach this matter holistically , then yes Muslims and Christians do not believe in the same Jesus since their beliefs on Jesus (pbuh) and his ministry conflict with each other however this approach is flawed because both Christians and Muslims are speaking about the same historical figure.
"while the “Jesus of Islam” never suffered or died because as a prophet of Allah, he could not suffer or die a horrible death. That is the teaching of Islam."
Islam definitely teaches that Jesus (pbuh) did not die on the cross.
That they said (in boast), "We killed Christ Jesus the son of Mary, the Messenger of Allah";- but they killed him not, nor crucified him, but so it was made to appear to them, and those who differ therein are full of doubts, with no (certain) knowledge, but only conjecture to follow, for of a surety they killed him not [Sura 4 : 157 , YUSUFALI Translation of the Quran]
but the reason Hussein gives us is false in the light of Islam , the Quran does not say that Jesus (pbuh) did not suffer because he was a prophet of Allah (swt) , Islam teaches that the prophets (peace be upon the all) suffered ridicule , rejection , hardships and even physical assaults because of their missions , Jesus (pbuh) is no exception.
Allah (swt) in his wisdom deals with certain evildoers who try to plot against him by plotting against them as a punishment.
And (the unbelievers) plotted and planned, and Allah too planned, and the best of planners is Allah. [Sura 4 : 157 , YUSUFALI Translation of the Holy Quran]
This is the reason why Allah (swt) saved Jesus (pbuh) according to the Quran , we can see a similar case in the story of prophet Abraham (pbuh) , how his people tried to burn him alive but Allah (swt) saved him from their plan.
"Fie upon you, and upon the things that ye worship besides Allah. Have ye no sense?" , They said "Burn him and protect your gods, If ye do (anything at all)!" , We said "O Fire! be thou cool, and (a means of) safety for Abraham!" , Then they sought a stratagem against him: but We made them the ones that lost most!" [Sura 21 : 67-70 , YUSUFALI Translation of the Holy Quran]
The case of Jesus (pbuh) is no different from the case Abraham (pbuh).
A prophet's mission is to proclaim the truth Allah (swt) has sent , the Quran does not teach that prophets can not die a horrible death on the hand of their enemies just because they are prophets , for example the Quran accuses the Jews many times of killing their own prophets.
When it is said to them, "Believe in what Allah Hath sent down, "they say, "We believe in what was sent down to us:" yet they reject all besides, even if it be Truth confirming what is with them. Say: "Why then have ye slain the prophets of Allah in times gone by, if ye did indeed believe?" [Sura 2 : 91 , YUSUFALI Translation of the Holy Quran]
As to those who deny the Signs of Allah and in defiance of right, slay the prophets, and slay those who teach just dealing with mankind, announce to them a grievous penalty. [Sura 3:21 , YUSUFALI Translation of the Holy Quran]
They (also) said: "(Allah) took our promise not to believe in an apostle unless He showed us a sacrifice consumed by Fire (From heaven)." Say: "There came to you apostles before me, with clear Signs and even with what ye ask for: why then did ye slay them, if ye speak the truth?" [Sura 3:183 , YUSUFALI Translation of the Holy Quran]
Allah(swt) in his wisdom knows the best in this matter.
"However, one thing that you should know, and Muslims do not tell anyone, Prophet Muhammad died a horrible death. He was a prophet of Allah, and you think he was spared from anguish, right? Not quite. He suffered for more than three years and died. A Jewish woman poisoned him; he suffered from complications for more than three years and died a terrible death. Now there is a prophet of Allah who the Hadith shows died a horrible death."
Hussein is aware of this article (I strongly recommend reading it for true facts) since he quotes it over here.
"Does the Prophet's Death from Poison Disprove His Prophethood Or Was It An Honorable Death For Our Beloved Prophet? By Bassam Zawadi"
"Muslims should quit denying that Jesus Christ died and resurrected because Jesus Christ is not the “Jesus of Islam” who, in spite of all the excellent attributes he had more than Prophet Muhammad, played a second fiddle to Muhammad. What a joke!"
Once we are presented with sufficient facts about the alleged "death and resurrection" of Jesus (pbuh) we will stop denying these so called "truths".
Prophets in Islam have different titles and attributes , these titles and attributes do not determine how great a prophet is , what determines that is the mission of that prophet and according to Islam no prophet had a greater mission than Prophet Muhammad (pbuh).
"Only Muhammad would claim to be getting revelations from God to refute something like the death of Jesus Christ, which happened 600 years before Muhammad was even born, and then set the conditions for how a prophet of his god should live and die (honorably) and then die in a miserable way. That is Islam for you."
The "death" of Jesus Christ (pbuh) has been challenged centuries before prophet Muhammad (pbuh) was sent , we know this from the writings of early church fathers and the extreme diversity of 1st century Christianity.
The fact that the events in question happened 600 years before prophet Muhammad (pbuh) does not mean anything as long as the evidence for the Quran being the word of God still stands strong , it doesn't matter if the time difference is six hundred or six million , and this is not fallacious or false reasoning even from the Christian side , according to the Christians Moses (pbuh) allegedly wrote the first 5 books of the Bible aka "The Torah" or "The Pentateuch"  , in that book we find the alleged stories of prophets like Noah (pbuh) , a question comes into mind , how long is the time difference between prophet Moses (pbuh) who is allegedly writing these stories and prophet Noah (pbuh) ? it had to be several or dozens of centuries Allah(swt) knows best , yet we see the Christians accepting these stories on the basis of revelation , Muslims are no different.
In the light of Islam , all of Hussein's arguments are false and unreasonable to begin with ,Muslims have no problem with the prophet Muhammad's death weather it was from poison or not , Islam does not teach that prophets don't suffer or do not die on the hands of their enemies , no wonder Hussein thinks Muslims "don't tell you" this "one thing".
 I do not deny that some Muslims use the argument Hussein is trying to refer to , mainly that "death by crucifixion is a horrible death thus Jesus (pbuh) was not crucified" however I am not convinced by this argument in the light of what I presented and history , there are better ways to refute the crucifixion.
 Although Christians believe prophet Moses (pbuh) wrote the first 5 books of the Bible (Genesis , Exodus , Leviticus , Numbers & Deuteronomy) but in reality Moses (pbuh) did not write those books as we have them today , we as Muslims do not deny that the original Torah was revealed to Moses (pbuh) , quoting from Dictionary of the Old Testament: Pentateuch by David W. Baker and T. Desmond Alexander:
"Although biblical scholarship is deeply divided on the issue of how the Pentateuch was composed, there is widespread agreement that the Pentateuch, as it now stands, is an edited work and not a piece of literature that was penned... by one individual" [Pages 61-62]
"While the long-standing tradition of Mosaic authorship is based upon clear statements that Moses was responsible for writing substantial parts of the Pentateuch, the weight of evidence suggests that Moses probably did not compose the Pentateuch as we now have it... This is not to say that the Pentateuch's claims concerning Moses' literary activity should be rejected. On the contrary, such assertions ought to be respected and given serious consideration, which unfortunately all too rarely happens," [Page 70]
The reason why I added this addendum is because Hussein brought to my attention some factors he believes I should have taken into consideration.
Hussein is having a debate with a certain Muslim brother in the comment section of his original article , they are discussing many different issues and Hussein frankly isn't bringing any new objective arguments to the table see for yourself and judge (rehashing arguments like the mariamite trinity and the sister of Aron) , this is a public discussion between those two and I do not wish to get in the middle but I will say that Muslims have been successfully refuting many of Hussein's allegations for 1400 years now , however they did discuss some issues related to the article itself , I will be responding to those comments.
"A Muslim scholar, Saifur Rahman al-Mubarakpuri, has this to say on Prophet Muhammad’s death, “Pain grew so much severe that the trace of poison he had at Khaibar came to light. It was so sore that he said to ‘Aisha: “I still feel the painful effect of that food I tasted at Khaibar. I feel as if death is approaching.”"
I still do not see how this can refute my argument , my argument is that the poison was not the sole reason of the death of the Prophet , and even if it is , how does this disprove his prophet hood and on what authority ?
His website states, “A Research Institute was established in 1408 Hijrah at the Islamic University of Al-Madinah Al-Munawwarah as “The Center for the Services of the Prophet’s Biography.” I was selected to work there and was entrusted the duty of preparing an encyclopedia on the subject of the life history of the Noble Prophet (sallallahu’alayhi wasalaam)…”Now tell me, the Saudi government gave this Muslim scholar the task of preparing an encyclopedia on Prophet Muhammad’s life. He only mentioned poison once in his biography on Muhammad. He did not even aver that a Jewish woman had given the poisoned lamb to Muhammad. Is he a credible Muslim scholar? Does he meet your demand for a “credible” biographer of Prophet Muhammad? Why didn’t he mention the poisoning and the condition the woman gave of a prophet?
How many times did the prophet (pbuh) have the poison ? ONCE ! there is no need to keep mentioning it over and over again as if it was the sole reason of the death prophet Muhammad (pbuh) , the evidence does not show that.
I did not check out this biography to be honest , but if so , then the Muslim scholar is in fault.
"By the way, aHadith I linked to in the article show that the Jews woman was testing Prophet Muhammad to see if he were a genuine prophet and poison would not have affected him. Muslim scholars have written about his death but they do not show that the intention of the woman clearly was “if you are a prophet then the poison would not harm you.” Is it fair to say since he died of eating this poisoned sheep he was a false prophet?"
And on what authority did this Jewess test prophet Muhammad (pbuh) ? she made a allegation , but no Muslim or Muslim scholar would take it seriously as a criteria for prophet hood unless she or any Jew and Christian can provide any kind of authority for her claims , and no it is not fair to say he died of eating the poisoned sheep because they evidence does not suggest the poisoning to be the sole reason of the prophet's death.
This all reminds me of the alleged "true believer test" in the gospel of Mark , it says true believers will drink poison and not die  , 'till this day we haven't seen anyone take this test , does this mean all the Christians in the world are disbelievers ?
 The passage from Mark 16:17-18 is seriously doubted to be a part of the original gospel according to Mark , so it is possible to find Christians denying this test.