It's an unusual blend of both in pretty equal balance. You have the puzzle solving of the point & click adventures like broken sword/beneath a steel sky but then you also have the somewhat action oriented sections but for what may be the only time in the history of gaming, they don't screw it up and make a jarring switch between them that feels like 2 different games.
The adventure component is shown more often than the action parts but thats quite a lot down to play style. I'm a sneaky bugger and so prefer to slip in around guards but the option is there to go shooting them up and it's quite a viable tactic, often the easier option even with the fact that they rather rudely shoot back! There's a finite number of guards though so you don't have to worry about setting off alarms and being overwhelmed by infinitely respawning enemies.
The stealth is a bit weird, there's not really a major indication aside from a bit of shadow of when you're in stealth and when you're not but you get the hang of things pretty quickly and can get through stealthy parts with only a few "oopsI screwed up" reloads.