Martin Lloyd-Jones was against formal debates with unbelievers. Why? His first reason is that no one comes to faith through a debate. Thus, debates are not useful. However, though the debate opponent rarely comes to faith, Dr. William Lane Craig (who debates non-believers regularly) claims people in his audiences do so. Debates are not merely showdowns between two people with opposing views, but showcases of opposing views allowing audiences to to hear both sides.
Loyd-Jones then says that the topic of God is too serious a matter for public debate. I'm not clear what he means at this point. Isn't a 'formal' debate as serious as one can get? What would count as a serious venue for talking about God? Only church on Sunday morning? Only when preaching?
Finally, he suggests that unbelievers are so blinded by sin that they cannot talk about God (or cannot talk about him properly). But surely believers and unbelievers share enough common ground to begin a discussion about the existence of God, the resurrection of Christ, or the veracity of the Bible. An unbeliever does not share our inclination to worship God, but he or she can surely talk about Him.
Lloyd-Jones seems to think that formal debate trivializes the Christian faith. After all, debate is a form of entertainment. However, the fact that people are entertained by debates does not entail that a Christian apologist is always debating in order to entertain anyone. It may be the case that someone is entertained by a sermon, but that does not entail that the preacher has belittled his subject.
Thus, unless there is some Biblical command prohibiting formal public debate, I'm inclined to think that there is nothing sinful about participating in one.