Have had several of both over many years. Both are excellent rifles and both will outlast you if you take care of them.
One issue with the cast receivers in years past was that in NM competition, the constant adjustment of sights would, supposedly, wear down the detents and allow the rear sight to not hold zero correctly. Even if this was true (and it probably has some basis in fact), I can almost guarantee that not one shooter in 10,000 will ever have a problem with this.
The M14/M1A requires serious and expensive work from a very talented gunsmith to shoot its' best, but its' best is very good, indeed. Rack grade rifles display about the same accureay in both the M1A and FAL models, especially with surplus or "white box" ammo. Typically, the better sights and superior trigger of the M1A makes it easier to HIT with, even though the intrinsic accuracy is no better than...and sometimes not as good...as the FALs.
Use only GI mags with the M1A. Mark the mag(s) that show the best accuracy for more serious target work...yes, it can matter. GI mags work. Other crap out there won't. I have a box of 24 magazines I ordered long ago from an aftermarket mfg., all still new, that won't even lock into my NM rifle.
Both rifles should easily do 2 m.o.a. with decent ammo, and both are fun to shoot and well made. For SHTF use, the availability of excellent mags for the FAL plus the adjustable gas system has much to recommend it.
Me? I own and like both, but my choice for only one in today's market would be the FAL.