The one unit per hex switch essentially ruined multiplayer. Don't get me wrong, gameplay-wise, tactically, I love it. It works great in single-player. But multi-player, unlike single-player, is played out on "simultaneous turns." This speeds up gameplay, instead of everyone separately taking their turn, everyone moves at once, and there is usually a turn timer enabled. So, in previous Civs, when stacks were king, you simply had to trouble yourself with one army while you were engaged in war with another player. Sure, you might have two armies, or one army and a couple guys scattered around scouting the enemy base, but the meat of your army was usually concentrated in one or two tiles at all times.
Because of the simultaneous turns, there was often a "race" to see who could move a unit or a stack of units first. For example, if I have an army that I think can destroy an opposing player's army, I'd try to attack it, and he'd try to scamper across a river, or up a hill, or in a nearby forest tile to either escape or get a defensive bonus to mitigate my numerical advantage. This was all fine and dandy when you had more men but less tiles to worry about. I mean, if you have 100 men on a tile but they all move as one, then it's essentially just one big mega unit.
Now, with simultaneous turns, and one unit per hex, it becomes a huge problem. Your army is spread out. Each unit is far more valuable than what its counterpart would be in previous Civs. The tactical implications are much more vast of losing a unit, or taking a tile, or losing a tile, etc. The problem is of course, that the "race" to to move or attack first becomes ultra-critical. If my army is 7 units and I lose two because you got the jump on me, then I'm basically finished. With so many more tiles to deal with, and so little time, and so much at stake, it becomes a farce.
So, it's somewhat ironic that by trying to make the game more tactical, it had the reverse effect in multiplayer, where online warfare is largely a random affair based on whoever has less lag and can click faster.
Edit: The reason why it was less of a problem in Civ 4, is because you'd usually end a stack's turn on a defensible tile, and a stack would include a variety of units which consequently would make the stack more impervious to getting wiped out.
In Civ 5, because only one unit is allowed per hex, the fastest player to act can destroy the other (e.g. sending his pike against a horseman, etc.). To compound the problem, losing a unit in Civ 5 is much more devastating than it was in Civ 4. This creates a game where an entire war can be won or lost in the opening moments of one furious click-fest of a turn (inserted from a post below by way of further explanation).