I think it's like the difference between a 28" and 26" barrel on a shotgun. People generally find that the longer barrel is easier to point accurately. Of course, if you don't use the arrow to aim with, then it really doesn't matter.
Another advantage of a longer arrow is that it will lower your point on and therefore all your gaps at distances less than your point on will be smaller.
Another advantage, for target shooting, is that a longer arrow allows you to use a lighter weight point to get the same spine, meaning your arrow will have a flatter trajectory.
Of course, this could be a disadvantage for hunting, where you might want a shorter arrow that requires a heavier point to get the same spine. Howard Hill once said that any arrow sticking out in front of the bow at full draw was a waste.
For bows where my bowhand forefinger is close to the shelf, I prefer an arrow cut such that the back of the broadhead or the ridge at the back of the field point will touch my forefinger when I come to full draw, as a draw check. I believe Howard Hill also did this, which is probably why he preferred arrows that didn't extend much past the shelf at full draw.
I wish all my bow grips were like that, as I miss having a draw check on bows where my forefinger is considerably lower than the shelf, but the awkwardness of reaching my forefinger up to get a draw check seems to offset any good having the drawcheck might be doing for me.
So, as you can see, there are pros and cons.