Now obviously with my current setup there's a decent amount of lag. I was going to upgrade my graphics cards, but then it occured to me that my processor is aging as well. So, is a new graphics card or a new processor going to give a more noticable improvement in performance?
Overclock the CPU as its bottlenecking your setup. Which model x4 is it? The 4890's are not that bad. If you were to upgrade I'd OC your CPU (unless its the original Phenom, then you should upgrade) then spring for a 7850.
your cpu definitely needs to be upgraded if you want better gaming performance and a gpu upgrade would help as well but the ones you have are not so bad as said by smeg. The fx 8150 is not a really good gaming cpu but considering the fact that you probably have the motherboard to host one of them (needs am3+ socket) and that you are looking to pay as least as possible then th fx 8120 would be a better choice or if you want to wait for piledriver to come out it should not be long.
For the best gaming performance you probably know that intel is the best so if you really want to do some hardcore gaming it could be worth to spend more and buy an ivy bridge.