I have on several occasions, both as a Muslim and a Christian.
In the former case, my debate partners (more accurately, co-arguers) were Christians of the Protestant persuasion, and, to a man, ended up stomping away red-faced. I’ll tell you honestly that not one of the people had a decent apologetic: they were all fideists and, if the metaphor of cleanliness and Godliness holds, fideism is next to Satanism in my eye. Life and belief are about thought and conviction through reason, not through blind faith, which is idiocy. If someone can prove you wrong and you still believe, it’s blind faith.
All of them used the same, tired tactics: “see how Jesus has changed lives! see the Holy Spirit in action! it’s about faith! have a personal relationship with Jesus! enter in to a dialectical relationship with God!”: I didn’t care how Jesus has changed lives, I didn’t believe in the Holy Spirit; I never heard a real, live proponent with an apologetic of the type as, “this is how we know God exists; this is why the scriptures are reliable; this is the evidence for the resurrection; here are the prophecies; here is the textual evidence”, etc., which is the kind of evidence - especially of the philosophical and Thomistic varieties - that eventually brought me around and gave me conviction instead of going-through-the-motions.
Eventually one Protestant told me to “read the New Testament, and come back, and I’ll become a Muslim”, issued as a challenge - as if I couldn’t deal with it. It’s just a book. I took him up on the challenge to prove him wrong. I did read it with as open a mind as I could muster (“the book’s been corrupted and is obviously false, it has no power!”) but with Islamic and atheistical preconceptions. I had read the Old Testament in a Jewish translation (the NJPS) because I couldn’t stand the Christological interpretations of Christian Bibles. That day, I bought the cheapest Bible I could find (a plastic-covered text edition of the NRSV) and began reading at Matthew: if I remember, “This is the book of the generations of Jesus the Messiah, child of David, child of Abraham” - I was intrigued, given that Islam places so much emphasis on Abraham (more than anyone but Muhammad) and view David as a prophet who was given the Zabur (Psalms) as scripture.
Needless to say, he didn’t become a Muslim.
I never really believed in God, not even after that point, but I recognized the Jesus of the Gospels as something a human could never be, and, even if he was invented by the apostles, something a human could and would never dream up; they would write of a failed and noble king, much like Muhammad (except he was a successful king), not a person who preached values so disconsonant with our most basic instincts and beliefs. Because of the dissonance with human nature, it seemed impossible for a man to even have conceived such ideas, let alone have put them in the mouth of someone else, as everyone would have thought, “this character is obviously fictional”.
I read it. And I read it again. I read the Christian Old Testament, which, even in the poor NRSV translation, which mutes Christological prophecy and interpretation, and found myself more drawn to the opinion that it prefigured Jesus.
I read more about Christianity, and ended up reading the Summa Theologiae of St Thomas Aquinas, which was of ultimate importance in my conversion, and a few Papal encyclicals (namely, Fides et Ratio, which was of penultimate importance in my accepting the Catholic faith, given that it has an intellectual rigour not found elsewhere). I read a whole host of other apologetics books, Catholic and Protestant, from The New Evidence to Reasonable Faith and historical-critical commentaries to learn text criticism, variant readings, provenance, chains of transmission, etc. and found an intellectual openness and honesty completely absent from Islam; a dogmatics based on reason, instead of a reason based on dogmatics.
After Fides et Ratio and the Quinquae viae of Aquinas, I for the first time actually believed in a God.
Soon after, I reverted to my native faith, Eastern Orthodoxy, which I converted from as a young teenager due to a confluence of factors, with which he was none too pleased (being a “bible-believing evangelical”) but found much better than Mohammedanism (as do I; I use the word not as a slur but as a descriptor, since Muhammad thought it up in his imagination, it can have no truly objective reality).
The (unfinished: I’ve yet to be confirmed due to lack of transportation) journey from Orthodoxy to Catholicism is too long to fit in this post, and full of more theological technicalities.
As a Christian, I have debated Muslims, which always ends in being asked in a it’s-not-a-question-way, “You’re a paid operative of the Jews or Zionists, right?”, or “How much are they paying you?”. I’ve also debated with Protestants of an evangelical but more kindly-natured persuasion, and have yet to gain a convert to the Church, but have rebutted all arguments successfully, ending once in a pensive “I’ll have to get back to you on that” and once “The Devil is trying to snare us, the Whore of Babylon isn’t to be trusted” rhetoric.