For a .38 Super, you will NEED the Large Frame, due to the .38 Super being a bit longer of a cartridge than the 9x19mm.
In my direct experience, I've not found the difference between the Tanfoglio Large Frame and Small Frame to be a problem at all, for my medium sized hands. YMMV.
The Large Grip Frame is actually just a bit longer, but not wider.
If you have a chance to examine one at a Gun Shop, so much the better.