I'd say that "経験"describes experience as knowledge. Used in contexts like "Let me do it, I've got some experience."
On the other hand, 体験 describes the fact that you have been subject to something. It doesn't mean you know/understand it, just that you've tried it.
So, roughly, the nuance would be:
- 経験がある -> experimented;
- 体験がある -> has tried once.
P!