For gaming - no question it's the CFX 6870s. If you drop down to the 2500K to get that into your budget that's just a smart move IMO.
Encoding video - that's not so clear cut. Everything else being equal and using encoding software that uses lots of threads the i7 would lead the way.
But both options will do very good at encoding. One might do it a big faster, but both will get the job done very fast.