I have the Gamechanger .84 and the very first Kickstarter version of the Rockwell, which received a reissue of the top cap and plates after the serious problems with the original parts.
I find that the 6S gives me a perfectly good shave on 4, and, although it didn't matter at all on early use, and isn't a big issue now, I feel that the head bulk detracts from it a little bit. The Gamechanger scores on aesthetics and finish, is very "nifty" in manoeuvre, and shaves marginally better for me in every regard.
The multi-plate Rockwell approach is probably very useful for many users, but, speaking personally, as a "one plater", I don't make any use of the versatility, and I'd probably want to buy it with maybe just one or two plates. However, if I were forced to make a choice between the two, and with some experience of both, I'd go with the Gamechanger.