Well i would carry both on me if i had the choice so if i need to take some one from a far no problem from close up no problem either. But generally sniper would be better, kill target A run away to point B hide away from police at point C when every thing clears up go back to living at point D then go and kill target E and repeat cycle while going down the alphabet.
I like short to medium distance fighting with plentiful cover, because it gives you the most chances to use observation and tactics instead of just being accurate with the mouse. So I'd really want to say shotgun, but the problem is shotguns are crap in most games.
So, what, are we talking Halo 3 shotgun or COD 4 shotgun? In Halo 3, I would have to say shotgun. Same as in Left 4 Dead. It really depends on what you're aiming to do with your weapon. Gotta kill 100+ enemies at close range? Shotgun. Want to just stay alive like in Search and Destroy game modes? Camp it out with a sniper. It all depends on the situation.