Well, what with this discussion almost starting in that pencil thread, I figured why not start a new thread up for it so taht people could discuss one one they prefer and why.
I've used both of them, and although they're both really nice and you can get some sweet tonal ranges, I personally prefer conte. Other than the obvious fact that charcoal leaves such a massive mess, I just don't feel as comfortable with charcoal as with conte. I find that I can get stronger lines with conte, and with regards to tone, I've always found myself getting too dark when I use charcoal. Also, if you're not coordinated, you run a higher risk of smudging all over the piece with charcoal than with conte.
Again, these are just things I've found with my experience with the two media, and in no way am I saying that one is better than the other.
So, that being said, what does everyone else have to say on the subject?