It's kinda hard for me to answer the first question as I don't play a lot of stealth games, but I'd say it's mainly not so much about not being seen, as not having your cover blown. You can put on various disquises throughout the levels and "guards" will act differently based on what you're wearing, often allowing you to walk right through guarded doors in plain view.
My favourite thing about it has got to be all the creative ways you can kill the targets. Most routes are specific to the level, but they cover things as wide as poisoning the guy's food, to rigging a chandelier to fall on someone, to swapping out a fake gun with a real gun during a rehearsal for a play (my personal favourite). Of course you can always just go in and kill everyone you see if that's how you prefer to do it.
And nothing's better than the feeling of beating a level without being detected at all and causing no collateral damage.
Not to mention that the storyline is actually pretty good and well presented.
I should also probably say that I've only played Hitmans 3 and 4.