Interesting question with a lot of dimensions... First off, I'm pretty good from the sand, probably a bit better than your average mid single digit handicap, which surely influences my strategy WRT bunkers.
My overall strategy with "normal" bunkers you'd find in the US is that I don't worry about fairway bunkers if they are either within 150 yards of the green or further than perhaps 220 or so. The reasoning being that within 150 they are pretty easy to recover from and further than 220 or so I'm assuming I'm hitting driver off a par 5 and using a shorter club for more accuracy won't help because then I'd take myself out of range of hitting the green anyway. May as well risk it and figure I can lay up out of the bunker pretty much as well as from the fairway (if it is a tricky/tight layup I might reconsider that) Between 150 & 220 they will affect my strategy sometimes, I might hit a 1 iron off the tee to stay short and not have to worry about them, or I might favor the other side of the fairway if there seems to be little penalty for being in the rough over there.
Around the green I ignore all "normal" bunkers unless their location/slope makes it nearly impossible to hope to get up and down.
The no man's land of bunkers that are further than 35 yards from the pin and less than 80 yards is to be avoided because that's a finesse shot that Annika Sorenstam is apparently much better at than most of us
When they get "deep" things can change. I really don't care too much about depth per se, if I am in a bunker that's 10 feet deep but I'm 15 feet from the lip it isn't that hard of a shot, other than making gauging distance harder because its a blind shot. Its when you gotta get it up really quickly that things become more difficult, like your prototypical Scottish pot bunker. So its "deep" along with "steep" that makes me think.
Such a fairway bunker is to be avoided at all costs, as you essentially give up a stroke since you can only recover 20 yards or so, give or take. If you really get screwed or try to bite off too much, its a two or more stroke penalty and you may as well have just hit it OB! Around the greens they aren't quite as bad, because you aren't giving up a stroke with a good recovery, but it sure makes things harder, and you have to be careful of trying to do too much in an effort to get up and down when you should play for 20-30 feet away and take your medicine.
A "deep without steep" can still affect strategy if the lay of the land dictates that the ball is likely to roll into it and leave you near a steep lip quite often. You see this mostly with a deep bunker to the left or right of a green where if you just miss the green and dribble into the bunker it rolls down the slope and ends up where you have to get it up quickly to recover. The saving grace for such bunkers in the US is that the slope is sand and not sod and thus you stop before you reach a level lie -- that upslope makes recovery MUCH easier. I still wouldn't tempt fate with such a bunker, but I'll take it over a deep Scottish pot bunker anyday where the desire for low score is concerned.
The US needs tougher bunkers, most of them are just decorative and don't affecdt play for better players much. For poor players it sometimes seems as though it doesn't make much difference whether the bunker is one most of us would consider easy or devilish, they get psyched out and have just as tough of a time!