I think you can pretty easily distinguish stairs climbed using just the accelerometer, but I could be way off. I'd be impressed if a barometer had enough resolution to indicate smaller (~10ft) altitude changes.
The barometers in Android and iOS devices can usually detect altitude changes as small as a few centimeters! Although I wouldn't say that deltas that small are reliable. I think you can get a reliable, trusted altitude delta as small as about half a meter.