I keep a Wera Kraftform Kompact bit driver in my handbox. It covers a lot of terrain, weighs practically nothing and comes with a handy pouch. Also works with Vessel JIS-friendly bits and any other 1/4 hex bit you can throw at it.
No problems with the oily hands: The Wera's collar locks bits in securely with the slightest pressure and when you're ready to switch, you just push on the rubber-contoured collar and it ejects the bit. I feel bad getting the thing dirty, but that's just because it looks so awesome.
With a square-drive adapter, I can use my Wera bit driver and any conventional socket to make a pretty good nutdriver, and I can use locking extensions to get any length I need.
The Wera bits are great, and Vessel bits are extremely high quality, too. I have a Vessel 00 Phillips that makes the bit driver an excellent precision driver for old cameras and such. So much better than those crappy, tiny metal drivers.
There is a tiny bit of wobble with the bit drivers, but I haven't found it severe enough to be a detriment in any way.
I have a set of screwdrivers I keep in the house, but short of using them as a makeshift pry bar (which is stupid anyway), I don't think there's anything they can do that my Wera can't. It's just too convenient.
Now, if you need a long-shaft screwdriver and all you have is a bit driver, you're in trouble. For most duties, though, it does what I need it to.
Oh, and there's no striking plate for obvious reasons, so if I were starting from scratch and getting a bit driver, I'd probably make sure that the conventional drivers had a striking plate or whatever if you ever find yourself needing to tap them to dig into tough screws. Beyond the bit driver having a soft, rubbery/plastic back end, striking it, I'd think, would be pretty bad for the locking collar.