The difference really has almost nothing to do with the units of measurement (they're both angles), and a lot to do with the fashion of the day in scope manufacturing.
For historical reasons, MOA scopes will (almost?) always have fractional adjustments - 1/8 MOA, 1/4 MOA. Mil scopes will have decimal adjustments - .1 mil, .05 mil. Because of that convention, MOA scopes will have a finer adjustment resolution than their mil counterparts (.1 mil is a larger angle than 1/4 MOA). Whether or not that is a good thing is up to you. If you are not comfortable adding fractions in your head, that's a ding against MOA scopes, but this has NOTHING to do with MOA, and everything to do with fractions.
If you like to think in metric, there are some plusses to the mil units as well. 1 mil = 1 meter at 1000 meters. Yes, the same thing is true in inches (1 mil = 1 inch at 1000 inches), but when is the last time you thought about the range to target in inches or group sizes in yards?
If you like to think in inches and 100's of yards, the MOA has some plusses in that 1 MOA is about 1 inch at 100 yards.
Back to the fashion of it all, KD competitors tend to use MOA (again - history). "Tactical" shooters tend to use mils (I'm guessing because the military likes metric stuff like mils, and if the military does it, it has to be good, right?)
Both are perfectly good.