Generally speaking
not much, as .38 Special loads tend to use fast powders. Same reason most autoloader cartridges don't gain much in carbines.
Given the .38 Special's large case capacity (relative to it's "power level"), one could load .38 or .38+P loads using slower burning powders usually seen in low-to-midrange .357 Magnums, and you'd then get a significant gain in speed. However, the only powder I've tried this with, Blue Dot, doesn't burn at all well at .38 Special pressures.
The largest gains are seen with full-tilt, rip-snortin' magnum loads using the slowest powders. Loading such loads in .38 Special brass isn't wise. Some won't even fit, and if they do, it's still not wise.
All of that being said, the .38 Special in a Marlin 1894 is simply a joy to shoot. Accurate, virtually recoilless, shoots like a big .22. Dandy on small game, too. Me likey.
--Shannon