I am a big M1/M1A fan but there are certain issues which need addressing.
It is quite easy to scope a flat-top AR10. The M1A requires a 'good' scope mount that is not cheap (the not-good ones come loose). Now most competition with M1A's uses iron sights (NRA highpower bullseye etc.) so that may not be an issue for you. Conversely a flat-top AR10 may require buying pricey iron sights (good 1 MOA click-adjustable ones).
The AR10 does not have a stock bedding issue. This is the one big bugaboo for a competition rifle that fires a lot of rounds. The M1A/M14 action has a small recoil lug bedding surface (smaller than the M1 rifle) and generally needs to be re-glass-bedded every season or more for a high-volume shooter (this is the major source of the extra-rifles comments by Jack Roberts).
The trigger on an M1A can be made quite crisp and manageable at 4.5 pounds pull. But, an AR10 might have available replacement trigger units that can go way under that weight.
Magazine cost is another issue, not sure what AR10 mags cost but GI M14 mags might be available for under $30.
AR10's can be made sub-MOA from the factory. An M1A Super Match factory rifle might cost quite a bit more than such an AR10 (I'm not sure). If you buy a mil-spec M1A and try to build a match rifle out of it, you'll A) be lucky to get 1 MOA or better accuracy and B) swallow your tongue at the cost.
That said, I hate the feel of AR's and love the feel of M1's and M1A/M14's. (Now THAT'S a RIFLE!!)