As somewhat of a SC fan I must point out a few things:
1. Because a SC bass has a longer upper (non)horn, usually the balance is often better. Especially with a bass like a Warwick Thumb, the SC variant actually is well balanced, where the normal Thumb is not imo.
2. More wood equals more mass, which does make a difference sound wise. Not saying it is better, but it is different (just like creating cavities changes the tonal character).
3. A SC bass can have a deeper cutaway to enable better access to higher registers. Try reaching the 21st fret on a Precision...... it's hard.
4. It's just a different shape, not all basses need to look like a JB. If it's been acceptable for years on Guitars (LES PAUL ANYONE?), why not on Basses?
Need I go on? For the SC hater, I must admit that some examples are FUGLY as.....