In favour of the 4570:
1. Stronger performance per-core.
2. Lower TDP.
3. Longer-lasting processor socket (The AM3+ used by the 8350 may not have much time left).
In favour of the 8350:
1. Stronger multi-threaded performance.
2. Unlocked multiplier.
3. Cheaper to buy (just about).
In gaming terms I'd favour the 4570 on the basis that a lot of games don't fully utilise four cores, so single-core performance is more important than the amount of cores (or threads) available. Only newer games such as Watch Dogs will make use of the extra resources.
For multimedia work (particularly HD video) the 8350 would be the better choice due to its good multi-threaded performance.
Bear in mind that a good GPU and sufficient amount of RAM are equally as important as a good CPU, particularly for gaming. The choices you make here depend on whatever function is more important to you. If it's gaming you should priortise the GPU. If it's multimedia work, it's the RAM.