See, I've never personally found the accidental kills to be all that engaging. While the idea of getting out clean is cool, most of the accidental kills (other than pushing people down stairs or over railings) amount to little more than pressing X in two or three locations and then being told that your mission objective has been updated.Blood Money is actually a game I've beaten a couple of times, so maybe I'm biased, but I still feel it's probably the best one because you're encouraged to use "accidental" kills like poisoning and prop manipulation, which feel the most ironic, humourous and satisfying.
In all three games, my favorite way to dispatch a target is whipping out a silenced pistol and planting a bullet between their eyes before they even realize what is happening. It makes me feel like a badass, and I think the Hitman series captures that particular method of execution better than anyone else.