The AR10s can be found a little more cheaply as the EA-10s ($999 retail, about $850-900 at a nice dealer), and you don't give up too much, so that's always an option to consider. (you can buy the SS or chrome lined upper later)
Pros for the AR10:
It's a big AR15 -- It's accurate. If you can maintain one, you can maintain the other. You can go from a run-and-gun carbine to a 24" target rifle in under a minute if you have the upper handy. Optics are eay to mount, and you don't have to worry about losing zero when you clean the gun. If your armorer can work on one, he can work on the other. Some parts are similar enough to interchange. Great iron sights if you prefer to go that way.
Cons for the AR10:
It's a big AR15 -- If you consider the AR15 to be a flawed design, then the AR10 is flawed too (though the extra impulse from the .308 helps things). Also, just because the parts are similar doesn't mean all of them interchange. The AR10-specific parts are more expensive across the board, and there's only one or two outlets for the parts, depending on the part (Knight's or ArmaLite). Mags are tres expensive.
Pros for the FAL:
Easy to maintain. Quality parts are available semi-readily. Lower quality parts are available readily. Reliable. Some of the scope mounts make mouting easy and they hold zero pretty well. Cheap mags. Not as fussy about cheao ammo as an AR10 in some people's experience. (but not in mine... my AR10 and FAL will eat the same diet without problems, and dislike the same brands... FWIW) Adjustable gas system adds more theoretical reliabity (again.... this is not my experience, but enough people repeat it, so I guess it's true) There is nothing you can do to really hurt the gun... if the bolt locks up, you can kick the hell out of the charging handle, and it will come free... you may hurt the plastic knob, but the gun will be fine... I would not do that with an AR10.
Cons for the FAL:
Irons are so-so (though they beat the hell out of the irons on any AK or other buckhorn sight). You've got to be a little more vigilant with knowing what outfit originally put it together (though now that ASA and Hesse have AR10s on the market... you gotta think about those too). Accuracy is just ok. Some of the scope mounts may seem to interfere a little with cleaning (or at least getting a good look at everything) and can be a pain to remove, even if they keep zero.
The big fact will be what your intended use of the gun is. If it's for protection, then the FAL. If it's just to horse around at the range, rhen the FAL. If it's to hunt pigs, then the FAL. If you're wanting to do more serious target shooting, then the AR10. If you want to hunt deer, then the AR10. If you want to compete, then the AR10.
Again, IME, except for being cheap to buy new parts and magazines for, there's not a lot that my FAL will do that my AR10 won't, and my AR10's a more accurate rifle. My expereince may be atypical.