The first aspect is I guess shared with Nobilis, but the way Chuubo's expressed it got through to me more. Fate has a system where, after exhausting some "stress" boxes, you take different levels of consequences from attacks; if you face an attack and are out of stress boxes and consequences, you're taken out. The Chuubo's system looks superficially the same, but I think there's a subtle difference. Health Levels are described not in terms of consequences that someone inflicts on you, but as some sort of last-ditch defense you muster to keep from your antagonist getting what they wanted. This is interesting in two ways: it moves the creative decision from the GM to the player, and it makes wounds more active narratively. If someone tries to shoot you but you use a health level to survive, it's up to you if you dodge at the last minute and end up with a bloody but not-so-serious injury, or if the bullet is deflected by the pocket watch that was a gift from your true love, or if you take the bullet straight on but your amazing willpower lets you continue to function despite this potentially-fatal injury. If a vampire ambushes you and sucks your blood to make you a minion, you could have it fail because of your extra-thick scarf preventing your blood from getting sucked properly, or have it work but have the supreme goodness of your blood help you maintain your free will completely, or have it work but use your willpower to re-assert your old self at key moments. (Of course, there's still presumably some need for GM buy-in.)
The second thing is about recovery. I've struggled with consequence/wound recovery in the past. Recovering from a serious wound shouldn't be instant, but having the timing feel right is tricky. If you do it based on in-game time, then you either feel like a dick by having unavoidable events interrupt while the character is trying to recover, or you do accelerated downtime until they heal and the recovery seems quick. If you do it based on real-world time, you can end up with recovery times that don't make sense with the narrative of the story. (Part of my problem with this historically has been a tendency to have events flow in a continuous stream, rather than drawing clear "book" or "episode" breaks.) Either way, wounds can feel more like an obstacle to the story progressing than a contribution.
Chuubo's solves this in a way I super like: for deadly wounds, recovery is a quest. I like this because I'm all over quests, and given interesting wounds undergoing an active adventure to recover rather than just lying in bed/the hospital for a while seems way more interesting narratively. Though, from one perspective, you could see this as like negative levels in D&D, which I've historically disliked, because the experience you put into the recovery quest isn't going to your normal arc quest. I think Chuubo's not being "Grr argh everyone should be the same level!" makes me less concerned about this. Also, if you can make the story work out, you can choose wound recovery as the reward for an arc quest, so while it is still a disadvantage as you're choosing this instead of some other perk, it's not necessarily an obstacle to the main plot and I don't think in practice it'll be so big a disadvantage as all that. (EDIT: It’s been pointed out that, since even non-arc quests count towards the XP total for arc completion, this is even less of an issue. You’re really only ever possibly missing out on a perk or extending your arc for narrative reasons.)
The third interesting thing is that wounds in Chuubo's are often mechanics-wise advantages to you. Fate has them wishy-washily be neutral in that they're aspects like anything else and you could theoretically invoke them or get fate points for having them compelled, but in practice wound aspects are generally either used against you or ignored. In Chuubo's, while wounds bring you closer to death, they can also give you a pretty nice temporary power, based on the sort of defense you chose, which could easily be something that protects you from further similar attacks or gives you some other useful ability. I haven't seen how this works in practice, and the Chuubo's implementation has lots of hair, but it seems like it could be cool.
So, yay wounds!