One difference would be the lens used. Most of the 35mm-only enlargers I've seen come with a 50mm or so lens. 6x6 would require a longer lens - more like 85mm or so. The longer lens could be used with the 35mm, in fact, some say it's better to use somewhat long lenses, but I don't think the 6x6 could use the shorter 50mm lens successfully.
j