1. There are definitely instruments where the B string (in particular) have nothing in common with the rest of the strings. You play the E (open or any fretted note) then go play any notes on the B, it sounds like a different bass.
2. I believe string tension sometimes alters the output to the point that some basses clearly are louder on certain strings.
I believe there is a fix. By this I mean by changing the maker of the string it MIGHT help.
3. Uneven tension on string due to the neck. I have no idea how this happens but most likely it's in conjunction with number 2. I noticed on one of my bass, not only was the output different on each string, the the tension was different no matter what string I put on. This makes me believe that it's a problem with the design of the bass itself. I am not going to name this particular bass I am having a problem but don't worry, you'll probably never come across it. If you must know, PM.
4. Preamp. I suspect that two of the basses I have an inherent problem with the wood/pre-amp combination. As I turn up the dials on the bass, the tone of each string starts to have more and more of problem number 1.
So there you go. I am sure the problems I mentioned aren't all that peculiar and it most likely has a lot more reasons than I just mentioned. Some basses I own that have none of the issues are: Dingwall Prima5, Super J5, Xotic Xj1t5, Fbass fret and fretless. These have none or very little of the problems mentioned above.