Macbook Air Vs. Macbook Pro?

What's up everyone! I just returned home from a 2 year service-mission, and I'm currently contemplating which mac I should buy to secure for myself the highest quality of performance (for League of Legends), for the best deal possible. I'm planning on buying a mac for studies and other educational purposes. As I've been reading the past forum posts on this contemplation, I've noticed that a common, negative factor of the Air, is that it overheats quickly. Another common negativity on Macbooks in general, is that the FPS rate drops drastically in heavy team fights.

My question for you is first - is there a drastic difference between Macbook Air Vs. Macbook Pro in regards to running League? And if so, what are the differences? Also, is there a Mac/Mac settings that would be powerful enough to defeat the negative variables (mentioned above) that are attached to mac-gaming?

If you could help me out with this, I would greatly appreciate it! Thank you!