Theres a difference between saying who's right and making clear what we believe. I'm not gonna waste my time pulling out the mistakes of other people's religion, but i think its productive to at least make clear what my own religion believes. Again, i couldn't care less what YOU believe, but dont get the wrong idea about what I believe.
As for Muslims believing that Jesus it he messiah.
"(remember) when the angels said: "O mary, verily God gives you glad tidings of a word (Be, and he was) from Him, his name will be the messiah Jesus, son of mary held in honour in this world and in the hereafter and he will be one of those who are near to Allah" (The Quran 3:45)
Doesn't matter what sect you are of Islam, its right there in the quran.
And about mohamed being better than Jesus (No uh! Jesus is better!!! No uh! Mohamed is!)
"The Messenger (Mohamed) believes in what has been sent down to him from his Lord, and the believers (do too). Each one believes in God, His angels, His books and His messengers. (They say), "We make no distinction between one another of His Messengers" - and they say, "We hear, and we obey. (we seek) Your forgiveness, our Lord, and to You is the return (of all)" (The Quran 2:285)
So there ya go. Cant say either is "better". And cant say that Christians are defined by "Those that believe that Jesus is the Mesiah".
I rest my case