The big difference (the slight mechanical differences already have been well discussed) is that, unless you have the proper license, you will be a guest of your favorite uncle for a while.
The original AR-15 was adopted first by the Air Force, since our role was somewhat different from the other forces. Hence a lighter weapon, seemingly easier to disassemble the main components, etc. And, the original was semi-auto. In this role, when one carried such a weapon, it was secondary, hence less ammo being carried: couldn't waste ammo with full auto.
The original conceptual design, of course incorporated full-auto, which subsequently was adopted, or forced on (depending whom you believe) the other forces. Lots of politics involved. Personally, I think the M-14 would still be appropriate for the Marines (thanks for picking me up, guys) and some Army units. Most of the Army would be ok with the M-16. The NAvy should still be M-14.