Mice and Mystics seems pretty streamlined compared to other co-op dungeon crawler games. I would say it compares best to something like Descent instead of Arkham Horror though--the board is composed of large tiles, each with many spaces on them, and your party is usually confined to one tile at a time. They're really spectacular-looking though, and while the spaces are generally grid-shaped, they vary in size and shape based on the 'terrain' of the tile, so it looks really natural.
Gameplay-wise, each character has four stats: Offense, Defense, Lore and Move. Offense and Defense affect the dice rolled in combat and equipped weapons or armor are added to the score. For each point you get to roll one die in combat. All the dice are the same and have 1 sword icon, 2 sword/shield icons, 2 bow icons and 1 cheese icon. Swords hit in melee combat, bows do the same with ranged combat, shields block one enemy hit if you are defending, and if you roll a cheese icon when attacking or defending, you get a piece of cheese. Cheese acts as both Mana and Experience, in that you spend it to fuel your abilities, or you can spend 6 pieces all at once to "level up" and learn a new skill. Mice can level up as many times as you have the cheese to spend, but they are restricted to skills based on their "class". Of the seven mice so far, three have two classes and the rest have only one. Since there's only one copy of each skill card, you have to best determine which mouse should take overlapping skills. One good example of this is a skill called First Aid, which can be learned by any mouse, costs 2 cheese to use, and removes one point of damage from an adjacent mouse. However, if a "healer" class character learns this, it only costs one cheese to use. Therefore you have to determine whether you want a cheap heal skill and only one healer, or if you want to give it to someone else in order to have two mice capable of healing.
One thing I like about Descent as compared to M&M is that you roll different dice depending upon what you are doing or what you have equipped. Better armor gives you different dice. Because of this, getting new equipment feels fresh and fun. In M&M you just roll more of the same dice when you have better equipment. It's still fun, but it's different. You also are only allowed to keep one piece of equipment to carry over from chapter to chapter in addition to your starting equipment. Therefore you'll be searching for new stuff every chapter. If your mouse loses all its HP, it gets "captured" and when it is rescued (you defeat all the enemies on a tile) it comes back with only its default equipment. I prefer the equipment system in Descent to that of M&M, but M&M has such a cool theme, which is evident in every piece of equipment. Since you control mice, you might equip a helmet made of an acorn, or a sword made out of an old needle. Also, M&M is 100% co-op (like Arkham Horror) while Descent has one player controlling all the monsters. Unlike equipment, skills carry over from chapter to chapter, as do "Party Items" that you might acquire, so there is a sense of progression and growth for your characters.