Does anyone know if the figure itself is any different between the "With base" releases and the standard versions?
Did you even look at the pics?


Yes, they are different. The "with Crait base" figure has the fancier paint deco/aps and it has premium soft goods for the robe/wrap (and possibly skirt under them). Plus the die-cast accessories.
Better paint aps, more soft goods, and die cast accessories are the big difference on the Luke and Kylo "with base" sets too. Each seems to have a bonus accessory too that the single release doesn't (saber hilt for Rey, extra hand for Luke, Helmet for Kylo).