BAC is Bindon Aiming Concept. It is basically your brain combining the unmagnified view of the target with the view of the illuminated reticle. It enables you to get the speed of an unmagnified dot sight, and the target idenification of a magnified optic. Now how close it comes to speed of an Aimpoint or an Eotech can be debated for years. The same can be said for target id, that a higher power scope will be better at target ID instead of just 3.5X, or 4X, or 5.5x of any of the full-size ACOGs. They are very good optics, and the price shows it.
As for compact or full size, it really depends on what you are doing and wether you have a carry handle upper or a flat-top. For the price difference, it is not that hard to step up to a full size ACOG, in my opinion.
For all your questions, I refer you to the tacked topics at the top of this board.