Well Bioshock basically doesnt have any stealth in it whatsoever. I mean you can have people not notice you, but the second someone goes hostile, the entire room goes hostile and knows where you are. So yeah, Bioshock has "bad stealth" because stealth is virtually non existent in that game (you can get some gene tonics in the first two that make you harder to detect, but again, once you start a battle the whole room will attack). As far as shooting goes, I wouldnt say bioshock has bad shooting at all, I mean the games get pretty friggen intense during the action scenes.
I guess you can say the newest bioshock (infinite) has somewhat 'outdated' shooting. As in they havent really changed any mechanics from the old bioshocks, whereas other shooter games like Battlefield for example changes up their whole system, but really it's not bad by any means.
Games that have bad shooting would be the Call of duty franchise. The guns (even the big ones) have almost no kickback whatsoever, aim is always perfectly straight, cheesy magnetic knife physics. That's because the COD games really havent advanced anything in the last 4 titles as far as mechanics behind the scenes goes, so the shooter system in those games are very primitave as opposed to now a days quality in shooting games (i mean COD wouldnt be bad if it was 2004 for example).
A game with good shooting would be Rainbow Six Vegas. Great cover system, realistic gameplay, hard as [censored], drastic differences in guns. And those games are outdated now, but honestly i havent seen too many games that have topped it as far as shooting goes.
A game with good stealth would be Dishonoured or Metal Gear Solid, or any game that centres around stealth (from what i heard the last of us has a decent stealth system, still havent played it yet, havent been that interested but i will try it one of these days). I've never played Metro so i dont know how that game works as far as shooting and stealth goes.
But bad stealth to me, would be enemies that psychically know where you are the second you make a noise or 'get caught' by one dude, enemies centre around your location when looking for you (but dont know you're there) like GTA IV and V, enemies dont see you cus you're standing in a semi dark shadow in a corner 5 feet infront of them (skyrim and oblivion) and such things like that.
I guess the more "real" it feels when it comes to stealth is what makes me think it's good. Like having a dude in skyrim take an arrow to the face then be "must be my imagination" then go back to normal is a good example of something feeling really fake and not a good stealth system (though the ES games can afford to have somewhat [censored] stealth, as that is only one small aspect of the game).