It depends on the game you're planning to play. In some games, AMD FX processors lag behind the current Haswell & Skylake chips (although they do compare favorably to the Sandy Bridge & Ivy Bridge chips that also came out when the FX chips were released). In other games, there's little to zero difference in performance between Skylake i5/i7 chips & the FX chips -- like Titanfall 2 (http://www.techspot.com/review/1271-titanfall-2-pc-benchmarks/page3.html) & Battlefield 1 (http://www.techspot.com/review/1267-battlefield-1-benchmarks/page4.html). And some games even show i5s struggling to perform as well as i7 chips, like Gears of War 4 (http://www.techspot.com/review/1263-gears-of-war-4-benchmarks/page4.html). So while it's possible to be technically telling the truth by saying that "Intel chips beat AMD chips", the actual margin of victory for the Intel chips varies quite a bit.
However, before anyone can say whether or not you can improve anything on your system, we would need to know the following:
1. What are the current specs -- CPU, motherboard, GPU, RAM, etc.?
2. What is your available budget for upgrades?
3. What particular games are you looking at improving performance in?