That one seems to be the best at that price. Game-Debate says the graphics card should be enough to run BF3 and Crysis 3 at medium-high settings, but BF4 may suffer from low FPS. The i3 may have a tougher time as well, but the games should be playable.
The differences between i3, i5, and i7 are that the i3 has a static base clock, the i5 has a boost clock (will do so automatically when needed), and the i7 is a quad core and has a boost clock. Definitely go for the i5, but the 7670m is not better than the 8750m or 8670m.