The major third tuning idea is something I've toyed with on occasion, but never really stuck to simply because it would require way too much relearning of the instrument (same reason why I've shied away from 5th tuning). The advantage, of course, is that the entire chromatic scale becomes available in a single one-finger-per-fret position. Here's a little rap on the whole idea for guitar:
The Major 3rd Tuning
Now, one of the big drawbacks (in my mind, at least) of major third tuning on bass versus guitar is that chords become very difficult to get sounding nice. Because the intervals are a lot tighter, chord voicings can't be as spread, and generally everything gets muddled. This is OK on guitar, since the range is a lot higher and tighter sounding voicings are nice, but not so much bass. Also, you'd need a 5 string to have roughly the same range as a regular bass (EG#CEG#, so one semitone higher on the upper string).
It's an interesting idea, I've just never messed with it enough to figure out if it's worth it.
