The performance isn't too different. I think I should stick with the 7850 like you said to stay close to my budget.
Would the AMD FX-4300 cause any significant bottle-necking with the 7850?
The CPU and GPU should work well together and both overclock well. Best of all, the HD 7850 includes BioShock Infinite, Crysis 3, and Far Cry 3: Blood Dragon whereas the GTX 660 currently has no active promos.
Also, this bundle at Newegg enables you to pickup the CORSAIR CX500 + Corsair Carbide Series 300R
for only $105 which makes the CX500 only $5 more than the CX430