Which build is better for gaming?

I am building a pc in a couple of weeks and I want to get the best bang for my buck.

I have decided on two different builds.

7870 LE with amd FX 6300

or

7950 with 965BE.

Which will I get a better overall experience?

If you have a better build for $800 w/ Hawaii shipping then list yours.

So to save you time make sure it is under $730.

Note: I do alot of converting movies to VOB files and stuff for my Dad and I do a little bit of rendering here and there.

Note: I don't care what website it is as long as they are cheap and ship to Hawaii.

Get the 7870 LE, there have been benchmarks where it performs better than a 7950. And get the FX 6300, it's a great CPU and will not really bottleneck the 7870 like a old X4 965 will. 

You could also buy an APU like the quad core A10-5800K, it performs better than the 965. It has integrated graphics and if you want you can get another graphics card to run Hybrid Crossfire. I recommend getting a 7770 since it is just an awesome card and will work well with the APU. You'll be getting good FPS with this set up in BF3.

Just as a word of advice, builds with a better graphics card will almost always preform better for gaming than a build that has a better CPU. This of course has a few exceptions but that is the general rule. Most games are far more GPU dependant than anything else.