What's the maximum resolution on your monitor? If it is 1920x1080, the 6670 should still be great for running many games, but anything bigger and the 7970 is the stronger choice.

The 7970 is going to offer you a higher hash rate which is better for mining, but if you are just now getting into mining with a GPU make sure that you have an alternate use for it. If you just want some bitcoins, you might as well just buy them from BitInstant or mercaBit.eu because return on investment from mining is a long term proposition. Mining isn't a bad investment if you are counting on the value of bitcoin to continue increasing, but throwing everything you have into it is a risky proposition.