Big singles will have more of a huge Jazz bass sound, much louder, much brighter, and with lots of hum.
The Model J's will be more of a classic Jazz bass sound with the ability to switch between series and parallel wiring, and of course completely hum free.
I personally found the Big Singles waaaayyyy to bright for me.
Fuzzrocious Club #194
Brubaker Brute Squad #18
Spector Club #224 (USA NS-5MM, NS-2J)