Why not the FAL over the M14 or AR-10?
I have experience with all of the above, and the reason I go with the M-14 over the FAL is because it has better sights, a better trigger, and is more accurate. Of the two, the FAL is probably the most reliable, though not by much, and both are actually excellent in that category, so I don't consider reliability a determining factor... both are good enough IMO, and quite a bit better than the AR platform. With an M-14, it is possibly a little easier to clear malfunctions when they DO happen, with the reciprocating charging handle, ability to provide direct positive force on the bolt in either direction, and the open top receiver providing better access to the chamber area. Weight is certainly not a determining factor, as they weigh nearly the same.
The sights are probably the biggest determining factor for me... you just can't beat the M14's nice easy 1 MOA clicks for both windage and elevation right at the rear sight, with a BDC on the elevation knob going out to 1200m, and its outstanding sight radius. A Metric FAL has pretty good sights, and definitely better than a L1A1 pattern, but they still take tools to adjust, and the sight radius isn't as good. The rear sight is in the right place, right at the rear of the receiver, but they cheaped out and put the front sight on the gas block, instead of on the end of the barrel like they should have. The FAL is probably a little easier to mount optics on than an M-14... they usually don't end up needing as high of a cheek riser. But M14's aren't as hard to scope than some make them out to be.
As for the .308 AR's, they are more accurate than either the M14 or FAL, but not as reliable. I rate their sights in between the FAL and M14 (that's assuming a rifle length barrel and standard 20" sight radius). The triggers really vary by manufacturer, but you can put as good of a trigger as you want in it since they take AR-15 triggers. They are the easiest to mount optics on. They have no weight advantage on the FAL or the M14. It is the hardest to clear malfunctions with, with the 1-way non reciprocating bolt handle in an awkward position. The rest of the ergonomics are really good though, and mags drop free unlike on the other 2 rifles.
The G3 platform is highly reliable and inherently accurate (though probably not as accurate as most .308 ARs). However, they have poor sights -- I rate them worse than the FAL because they require tools for any adjustment except for switching between diopters, the diopters only go out to 400m, the 100m one is a wierd notch sight that is hard to use, and sight radius isn't any better than the FAL. Also they have horrible triggers. A lot of people don't like their ergonomics. Mags drop free though.
I rank them in this order:
M14
FAL
AR
G3
Just my .02... everyone has their preference. The important thing is to be skilled with whatever rifle you have. Any one of these will get the job done in capable hands. The M14 just makes the job the easiest for me.