Cato - SB-2's are nice basses for sure, and pack a lot of punch and bite. So far as tribbies go in general the necks are a littl thicker on the L series, so just check on the SB's what they are like, but they are definitely quality instruments.
Considering you use a Jazz bass already I'm interested in tonally what you are looking at (no disrespect meant in the question). The G&L Jazz basses are different to other Jazz's with G&L's pick ups being just awesome. There is the JB and the MJ which is wired and wound differently and is noise cancelling compared to the JB.
If its more of a passive P sound, but modern and aggressive then the SB-1 may be a good compliment on its own without the J element. If its traditional P, then LB-100 is your go to.
Whatever you decide, G&L is the way forward