It might help you understand the difference if you think of the 'chance' as meaning 'opportunity' in the first sentence and 'risk' in the second.

The first means I gave you a possibility of getting something good, not necessarily with risking anything myself. The second means I put myself at risk by counting on you getting something good, which wasn't necessarily certain.

"You took a chance on me" seems to always be used in reference to a relationship, and implies that the other person took a risk/chance being with you (in a relationship or otherwise). "You gave me a chance" doesn't necessarily have to do with a relationship, and puts the risk/chance on you since they gave you that power (by giving you that chance). Hopefully that helps...

I think they mean exactly the same thing. The only difference is the use of GAVE and TOOK. If it's about you, 'you' gave 'me'... If it's about me, 'you' TOOK a chance...