Good Benchmark comparisionhttp://www.anandtech.com/bench/Product/697?vs=702
For games, scoot to the botom list 4 games and FPS
Looks like about 20% gain favoring the i5 (I'm Not a gamer)
For productivity, look at what you do most often.
As to encoding/redering video, that may be just as dependent on the software as it is the core count. Reason is the lower end software (cost) may not take advantage of the full cores available.
My preference is the i5 choice, but not because of the CPU but Intel seams to have more frequent/better optimized chipset drivers.
I'd probably go with a i5-2500k (or i5-3750k), both only $20 more than the FX8350, and a Z77 MB. Then OC the the i5 to 4.2 GHz, which is very simple and most MBs have a one botton click to acieve this. This would put the two CPUs at the same speed and the diff would be less pronounced for encoding/redering and would increase the advantage (not a biggy) for i5 and gaming. Counter argument is that you can also OC the FX chip http://www.anandtech.com/bench/Product/697?vs=288
If encoding/rendering is what you do often then the AMD might be the better choice. However, i'd probably still go the i5 route as majority of all benchmarks seems to favor the I5 build.