Despite the obvious homage AoW owes MoM, the two are quite different in terms of how they play out. MoM is a 4X empire-building game in the style of Civ, while AoW is a more scenario-directed game in the style of Heroes and Warlords.
A marriage between MoM and Warlords would probably be the best way to describe AoW.
As for which one is better? That's a tough call. There's a lot I like about both.
Which one I prefer is AoW by a long shot because of one reason: Multiplayer functionality. Not only can it be played MP, it's FUN to play MP! I tried Implode's Multiplayer Edition once, and MoM is a game that just moves too slowly to be terribly fun with a couple of buddies, and its balance is so absurdly off that multiplayer isn't hugely feasible for it (also, I'm not sure on current status, but when I played it IME was still woefully incomplete).
But I'm not going to count that because it would ruin the discussion, and instead focus on single-player:
Pros for AoW:
More playable. This is a sort of vague category that sums up the fact that AoW has a better interface, quicker pace, gentler on beginners, and is all around easier to play.
Better balance: AoW is by no means a perfectly balanced game, but it's certainly better balanced than MoM. Balance isn't as important in Fantasy TBS games as it is in other genres, but it's still frustrating to see the huge difference in power between races and magic schools in MoM
Broader scale: Certainly not in concept, but in execution. AoW allows up to 8-12 players on a map, and up to 7 stacks in a battle. To me, this is probably its greatest strength. Being limited to 5 wizards and 2 stacks/battle is one of the greatest frustrations of MoM. It'd be great to give the game more scope, especially if in doing so they made a more robust (and logical) diplomacy system.
More replayability: Map editors and most recently (with SM) an RMG and relatively easy modability make AoW a game with more options to give the game a fresh breath of air once its gotten dry
Better AI: AoW Ai is still pretty crappy, but it's a fair shot better than MoM (which, given the age difference, is entirely unsurprising). I'd say that MoM on Impossible is more difficult than AoW on Emperor, but only because of Impossible's obscene benefits for AI - they're still dumb as bricks, they just cheat unrelentingly. MoM's Ai's tendency to send an endless parade of stupid little armies is the other frustrating part of the game - fending off 4 spearmen every turn just becomes tedious.
MoM Pros:
More of, well, just about everything: MoM has more races, more spells, more buildings, more options, more abilities... It's just got more.
Greater depth: MoM's got a ton of awesome stuff happening in it, with all sorts of interesting things going on. There are ten thousand different ways to play the game, and almost all of them are fun. I think this comes from MoM's focus on empire-building (More Civ-like), over AoW's emphasis on combat (more Warlords-like).
Spell of Mastery: If broader scope is the one thing I really wish MoM had, alternate victory conditions are the one thing I really wish AoW had. This adds so many more dimensions to the game, and presents an alternative for those who are tired of rushing out to crush their enemies. Plus it's created some nifty strategies, such as the infamous spellbook-free start.
Empire-Building: Covered partially above, but worth mentioning again. MoM's Civ-style gameplay is really at it's heart, and is one of the biggest reasons why it's still great.
More Interesting Magic: AoW's magic system is better balanced, but MoM's is, without question, more exciting. Late-game spells in AoW (especially 2 and SM) tend to be boring and not terribly earth-shattering, and tend to fall into a few basic categories. MoM's magic is much more broad, much more powerful, and much more captivating. In MoM, there's a real push to keep researching, because you never know what mighty spell could be lurking within the pages of your spellbook. Beyond direct damage, summons, and unit buffs, there's a slew of other fun spells, from Dark Rituals to Corruption to Lycanthropy to Altar of Battle to Gaia's Blessing... Things that you just don't really see in AoW - or any other game
I didn't mention visuals or music because those scales will obviously be tipped in the favour of AoW. I actually kind of prefer MoM's visuals over AoW SM, but the beautiful, hand-drawn art of AoW 1 trumps all. In my opinion, crappy animations aside, AoW 1 is the best looking fantasy TBS ever made..