Okay, because the comparison will inevitably be made. This game is NOTHING like Super Dungeon Explore. At least Version 1 and not SDE: Forgotten Kings because I haven't gotten that yet. It uses chibi miniatures and there are monsters etc but this game is best described as co-op pvp. Kind of. There's a lot more PVP than co-op really.
So just how does AQ play? Well, it's a bit like Zombicide or Imperial Assault really. You have these pregenerated mission maps that players choose. Each player leads a squad of 3 heroes and must try and complete the objectives specific to those maps. Once you do so, you can choose other mission maps.
Now each map has 2 PVE (player vs environment) quests that usually involves killing a certain monster or doing something random like finding a sword/switch/etc. These quests generally have certain in-game rewards; such as titles or equipment for your heroes. Then there are X PVP (player vs player) quests that basically involve killing an opponents hero; where X = number of players. That's right, to complete one of those quests, you will have to end up killing one of the opponents 3 heroes. No worries, they respawn.
To get past each Scenario, you'll have to complete at least 1 PVE quest so you can't just concentrate on killing each other. For a 4 player game, if any player completes 3 quests, the mission immediately ends. However, I've discovered (at least in my group) that most of the time, people will just complete the one mandatory PVE quest (and usually the easiest one at that) and then just wait to backstab each other at the most opportune time.
What this means is that games generally devolve into a free-for-all killfest, which is entertaining in its own way but it feels like that's the real meat of the game and that the other mechanics are a bit lacking. Like the monsters.
One of my main issues with the monsters in this game is the fact that they're really...kind of extraneous in terms of their impact on gameplay. The problem is that the monsters have a very limited AI. Even more limited than the zombicide ones, who will at least move towards survivors automatically. Instead, the monsters in AQ are more like decorations that occasionally get in your way. Why do I say this? Because in AQ, unless you attack a monster or move past him, monsters wil generally just ignore you. This means that in return, you're free to ignore monsters once a certain point in the mission has been reached; such as you clearing out the monsters from whatever path you need to take. Furthermore, monsters spawn so slowly, and sometimes not at all, that they never really feel like a threat. Instead, it's the other backstabbing humans you need to watch out for. As my friend put it "It feels like the monsters are the audience of a reality TV show watching human competitors try and kill each other".
Another interesting aspect of the game is how attacks/equipment is used. Each hero has 4 slots with which to equip attacks/equipment. Once an equipment has been used though, you're supposed to put a counter on it indicating it has been used and it can not be used until you use your turn to take a rest. At which point you remove counters from all used equipment. Which means that most equipment tend to be one-use until your next rest. This at least helps to prevent players from just spamming the most powerful weapon all the time. Unless you're the monk hero, at which point, as long as the person you want to hit is flanked by an enemy, your weapon doesn't get exhausted. Here's the kicker, other players and monsters count as enemies.
Which brings me to the heroes. Each hero has different HP, defense and special abilities. However, not all heroes are equal since some of the special abilities are situational enough that they really might as well not be there. In general, what you want in a Hero is HP first and then defense or special abilities. It's a toss-up between the two because it's generally pretty hard to roll a successful defense, which means it's not that useful overall although you'll still want some at least, and the fact that certain special abilities are pretty good.
Overall, I found the game amusing to play although that was really more from the PVP shenanigans and the random cussing of other players for backstabbing or killstealing. However, I feel that the mechanics aren't fully fleshed out and this really could use with a Version 2.0 or something in terms of how the monsters interact with the players.