So I took a lunch break and ran some serious A/B stuff.
Overall:
Level: Same - GS maybe gets a little louder.
Tone: When dimed, I think the TS is a little brighter, less bass. GS had a little more bottom all the time I think.
Gain: The GS was a little smoother overall, the TS was a little more ratty/raw. GS had maybe a touch more than the TS at the top end. Not much though.
I'd say the mid push in the TS was a touch more than the GS, but hard to tell.
All in all - they are both Tube Screamers. I could flip a coin and be happy with either. I think I may - may - prefer the GS a little more overall, but odds are good I'd grab my TS anyway out of habit. If I go for the GS, its just because its the new thing.