Not much. Ballistics are pretty comparable, the Super uses a semi-rimmed case that has lost most of its popularity over the many, many decades (1929), and the Super can be a lot more finicky about feeding. I can't claim ammo availability for either is any better than the other right now, but I do feel that the SIG has a definite edge in reliable feeding. The Super was designed to function in an 8 round 1911, and while it's a cool caliber to have, I think the SIG being designed for high capacity 9mm class pistols is a definite advantage. There aren't a lot of hi-cap Supers that have caught my notice, mostly competition "race" guns. Both use a weird case, the Supers case is unique, and the SIGs case is a necked down and shortened 10mm.
9mm has become so highly developed that it has some real advantages over both calibers. Velocity and energy are not among those advantages, but there are some really trick bullets for 9mm that simply don't appear to work well at 38 Super (+P), and 357 SIG top end velocities.