Major FPS Issue On Quad Core CPU But Not Dual Core - Same Model Computer

I owned a dual core version of this older L702x Dell XPS laptop. It had a 550m NVIDIA graphics card. On that computer, I could max out all graphics and easily maintain 60 FPS in League. Then I bought another L702x with a 555m instead, which is a bit faster of a graphics card with a couple more gigabytes of video RAM as well. AND...it came with a quad core CPU instead of a dual core.

Well ever since then, I've had to reduce my graphics to lower settings to get 60 FPS, and it seems like even that has gotten worse as more and more updates come out. But only for League. Every other game runs better since the upgrade...stuff like the Batman Arkham series. Shoot....I can run Batman Arkahm City at 1080p on low and get 45-50 FPS+ consistently. But League, everything has to be on low and very low when available, and FPS still drops to 30 or so sometimes. Something isn't right.

Is there something about this game that doesn't and never will work well on quad core processors? Or is it just my computer? I swear, the game ran flawlessly on a dual core CPU with a slower video card, so this is so frustrating.