Certainly the old Athlon II x3 will struggle with many game engines. It won't necessarily hold back your GTX 970 in everything though.
Luckily the Athlon II x3s have a lot of room for tweaking. The 4th core can possibly be unlocked, and there is a small chance for L3 cache to be unlocked as well. On top of that, some owners could overclock them stable to over 4GHz core and 3GHz CPU-NB.