I don't really know, as I don't have a Leopold so have never tried Cherry style stabilizers on a plate mounted board.
The stabilizers are the things on the long keys (2x and longer) that keep them from wobbling when you hit them off center. So really, only things like shift, enter, space, etc. would feel any different. Some people say the costar stabilizers give a more consistent feel (that is, they don't change the feel of the switch as much) but how much of that is true I don't know.
The other thing about Leopolds is they use a different spacing for the stabilizer posts on the space bar from Filco etc. but that is really only relevant if you are looking to get custom keycaps. If you are happy with the stock ones it's completely irrelevant.