Originally Posted by BFunk
They don't have less headroom, they have higher output. The device receiving the signal has fixed headroom, the amount of gain it can take before distortion. So a hotter signal is more likely to use up the available headroom. Headroom is actually a complex discussion that I won't get into here, but I think you get the idea.
While active basses often have higher output, there are plenty of low output active basses and high output passive ones. Just by adjusting pickup height you can make most active instruments have lower output at full volume than most passive ones.
I'm not talking about the device receiving the signal, I'm talking about the dynamic range of the signal being generated by the instrument. Passive instruments usually have a greater dynamic range than 9v active ones. Slapping or other hard right hand action often sounds compressed on 9v basses as compared to passive basses because the headroom of the preamp is being exceeded. That is one of the reasons 18v systems sound so much more like passive systems, because of greater headroom.