OK. I looked around for a picture of a JS LS Bass but was unsuccessful.
However I did find the following;
On the JS Bass you'll see that the overall length is 45-1/8" and the neck joins the body at the 18th fret.
On the JS LS Bass you'll see that the overall length is 47-1/4" and the neck joins the body at the 17th fret.
So if you do the math the LS is 2-1/8" longer.
Now the difference between the 34" scale and the 30-1/2" scale is 3-1/2".
Therefore, since the bass is only 2-1/8" longer and the scale is 3-1/2" longer, the difference has to be made up by moving the bridge back 1-3/8".
(Of course this is all bassed, no pun intended, on the catalog dimensions)
Also note that the nut width on the 30-1/2" scale is 1-1/2" and on the 34" scale 1-5/8"
I would then have to reason that the LS has a longer, and wider neck.