This is a position from a live chess game; Black just took a Knight on d5 with his Knight.  Is it better to recapture with the pawn, or the rook?  Please explain why one is better than the other.  Thanks.

i would do this:

I'd say it is better to take with the Rook as you keep the pressure on the weak d6 pawn as well as maintain the flexibility of your own pawns.  After 1. Rxd5 Ke7 2. Rhd1, Black can't hold onto the pawn and White will come crashing through.

Edit: Apparently, shiro_europa is faster with a diagram than I am with text.