I've owned a few of both, I only have M1A's now.
None of my FAL's were what I'd call accurate. Only one of three, a real FN, was reliable. If you get a "kit" gun, shoot it first and make sure it works, there's a lot of trash out there.
The M1A is accurate and reliable, and requires no fiddling with to shoot. It has very good, solid, repeatable sights, something most FAL's lack. Its also a truly ambidextrous rifle as it comes.
If you throw the HK91's in the mix. They win.