No, I don't drop my chain with my triple - although I hear some people have that problem with triples. I'm pretty good about not putting it in a cross over gear so that makes it less likely to drop - also when I'm going downhill, I gear up to my big chain ring in front to keep the tension on so that it does not bounce off on the bumps.

I would think that a compact would be good enough on a cross bike. It would be enough for me, but like I said, I ride a road bike with a 51 and 38 front chain rings.