MUCH more fun than you might expect.
The main criticism of the game is that's it's more of an interactive story than an actual game. When I saw that criticism, that almost caused me to write it off completely because for me, that's about the worst thing you can say about a game. I'm all about gameplay and interactivity, and I thought LA Noire was a very boring game for that very reason. I felt like a bystander more than a gamer.
So why is it different for Asura's wrath? I can't really put my finger on it, because it is true that it's light on the gameplay side and there's lots of quicktime events. But for some reason, it's still fun as hell to play regardless. It's separated into 'episodes' that are about 20-30 minutes each, and when you finish one episode you can't wait to get to the next one. I think part of why it's fun to play where (for me) LA Noire wasn't is because it's still challenging. You have these massive boss battles that are WAY over the top, and towards the end you have to be pretty skilled to beat 'em. So you get that sense of accomplishment when you win a big battle that was totally absent in LA Noire.
The combat is fairly varied. You have a standard melee, heavy melee, a dash attack, a dive attack, 2 kinds of ranged attacks (lock-on and free), you can dodge, parry (via quicktime), and there are 3 kinds of meters which build up via different reasons. Most of your battles will be against huge planet-sized bosses and they get tougher and tougher.
There's also a ratings system after each stage, and the better you do, the more unlocks you get. There's even 2 separate endings and a hidden episode, which you can only unlock by achieving an A-rating on at least 5 episodes. So even though the story lasts about 6 hours, there's more content here than that. You'll have reasons to replay this one.
I think that about covers it. The bottom line is, this game is much more fun than you would expect on paper. At the very least, do like I did and rent it.