I'm a low action guy for sure, but I think a lot of guys who double (play acoustic and electric) prefer their action a little higher - since the acoustic requires more effort to play generally, the higher action on the electric makes for an easier transition among the two instruments.
Patitucci, who is a doubler, has this discussion on his action preferences posted Link Removed. I've read something similar from Stanley Clarke as well:
STRING HEIGHT: For both acoustic and electric bass, you need enough clearance between the string and fingerboard so you can pull a sound out of your bass. If the string is too low and right on top of the fingerboard (or frets on the electric), your dynamic range between your softest and loudest sounds will be smaller. For the acoustic bass, the top of the bass won't vibrate as much and you won't be generating as much sound. You won't get as thick a sound and you may get noise when you dig in and have to play stronger.
For electric bass, again, I feel that the instrument must vibrate well, even though it is most often a solid piece of wood and there are pickups involved. It is still an instrument that is initially acoustic. So, you still need some room between the string and the fingerboard. It seems to me that many players sacrifice sound on both acoustic and electric, opting for convenience and greater ease of playing. You have to find the balance between ease of playing and getting a nice full sound with ample dynamic range. I have experimented a lot over the years and have my action on both instruments at a moderate place. I seem to have my action on electric higher than many players and more like my hero - James Jamerson (who played both acoustic and electric). This is not a value judgment, but a subjective preference.
Now, if the string is too high off the fingerboard on acoustic bass, you can actually wind up getting lots of noise, because you have to play so hard to get the note started. You can wind up with the top of the bass not vibrating freely because you are putting too much energy/sound pressure into that part of the bass and it starts to compress and vibrate less! Then, the irony is, getting a smaller and compressed sound when you wanted a large open sound. You can also hurt your hands, especially if your technique is not developed and you are playing with too much tension in both hands. Some people wind up with tendon problems, etc. Also, if the strings are too high, you will again have problems controlling your dynamic range, because you will have to play hard to get the note started and subtlety will be sacrificed. Pitch problems can also occur if your hand position gets compromised in your struggle to hold down the notes so they will sustain.
With the electric bass, if you have the action too high, you can even have pitch problems and sometimes pull the string sharp with your left hand. You have to be careful with your left hand if you are playing with too much tension, trying to hold the notes down. Some people get tendon problems from that. You also have to be careful not to play too hard with your right hand as it relates to where you set the pickup height - you don't want the string bouncing off the pickup because your action is higher and you are playing too hard with your right hand.