The FAL is probably a better battle rifle (I own both). The main reason it wasn't adopted by the US was because it wasn't invented here.
That being said, there are a few areas where the M14/M1A has some slight advantages.
1. Better iron sights. The click adjustable windage and elevation sights are awesome. Just like they were on the M1 Garand. The FAL does have some adjustment for elevation, and it works fairly well. However, it can only adjust for range in 100 meter increments and doesn't have the fine adjustment the M14 does. Windage adjustment requires a screwdriver and is not nearly as precise. Not something you can easily do when you are in the middle of shooting like you can with the M14. I'm sure this could be added to the FAL with a little engineering work. I have seen some home gunsmithing hacks where people have grafted on M1/M14 style rear sights onto an FAL lower. With some small design changes, this could have been added to the FAL as a factory option.
2. Better ergonomics for *some* people. If you prefer more traditional style rifles, the M14 is easier to adapt to. However, this advantage is small and most people probably wouldn't even notice it.
3. Seems slightly easier to use a sling. Slings work ok with both rifles as long as they have a front swivel installed. However, it seems to work just a tiny bit better with the M14. Of course this might just be subjective on my part.
The FAL has several areas where it has some advantages.
1. Easier to mount optics. Replace the dustcover and you are good to go.
2. Magazine changes are easier. Both rifles uses 20 round magazines that rock in, but it just seems like with the FAL it is easier to get them in properly.
3. More modular means it is easier to customize the furniture without replacing the entire stock system. It's still not as customizable as an AR, but then not much is.
4. Easier to clean. I always hate having to clean from the muzzle end. With the FAL, you can just unlatch the lower and upper and run a cleaning rod in from the back.
5. Looks cooler. Yes, I know that's a dumb reason.
Also, I'm talking about the base models. Not H20 Man's awesome custom setups.