^Keeping in mind that there are may different types of Buddhism, in general Buddhism has a far different World View.
I think it is difficult for you to imagine a Muslim Christian because it really isn't possible to be one. Someone who follows the teachings of Islam clearly does not give credence to Christian tradition and scripture and certainly denies the divinity of Christ.
I don't claim to be an authority on Buddhism, but there are some posters on this forum who are extremely knowledgeable on the subject. My opinion, however, is that the major Buddhist traditions (I'm most familiar with Theravada and Mahayana) are, in some ways, incompatible with practicing Christianity, in large part due to their perspective on the world, chronology, soul, etc. I have read arguments that Christ is, in fact, the Great Bodhisattva, or something along those lines, but that is not a particularly orthodox understanding. I guess, in a very similar vein as a recent Tai Chi/Yoga thread related to this, my question would be: Is Zen, removed from particularly Buddhist spiritual understandings, still really Buddhism?
I don't doubt that practices such as Zen, Yoga, Tai-Chi, etc have beneficial qualities, but I find it peculiar (please note that I did not write "wrong") that people want to somehow integrate these practices into Orthodox Christianity. I recognize the similarities between Zen and Hesychasm, but Hesychasm is also very different and was developed strictly within the confines of Christianity.
Take the Buddhist vs. the Christian view of Time. For a Buddhist all time is cyclical. Great circles that always come back around. In Christianity we understand time to be linear. There is a beginning, a middle and there will be an end.
This sort of presuppostion has great effect upon how to conduct ones spritual development. If I am to work off my Karma over many cycles of lifetimes, I can approach things one way. If I think I have one life and will face Judgement at the end of it, I will proceed a different way.
It isn't quite that simple. Buddhist time isn't cyclical -- if by cyclical you mean a process that proceeds to some point, then starts over again and repeats itself in the exact same fashion. Even the process of rebirth isn't cyclical in that sense -- you never simply repeat what you did in a past life. Likewise, in Orthodox Christianity, there is no end to time, because the process of theosis involves becoming more and more God-as-given-by-Grace. I can see Protestants arguing for an end to time, but not a theosis-based Christianity. Theosis has a beginning, but it has no end.
In Buddhism, at least in Theravada, the beginning of the whole process of one's life (and by "life" I mean all of one's series of existences, all of one's rebirths) is said to be "unknowable" or "unsee-able", and the realization of nibbana (which is the "end" of one's enslavement to greed, hatred, and delusion) is the transcendence, the end, of the whole process altogether, and entry into the indescribable nature of nibbana.
So, in Buddhism, there is an "end", and in Christianity, there is an "endlessness"; and, of course, vice versa is true as well. Traditions like Christianity and Buddhism escape any easy categorization of cyclical or non-cyclical, ending or non-ending.