The latter two of those games are known for that, as are many of today's games. Don't know about LoL, I don't play it.
We'd have a better idea whether there's an actual problem if you told us how the two sets of hardware compare on the same games.
New hardware ins't necessarily going to solve all your problems. It's getting quite common that PC games have big FPS dips.
Your 770 is pretty close to my 7970, and I get frequent FPS dips in both those games. Far Cry 4 seems to be far worse on AMD GPUs though. I've tried settings that yield 70-80 FPS and I still get the common intermittent hitching.
SoM plays relatively smoothly for me compared to FC4. I of course use High vs the Ultra textures though.