I own both the Fuji GX680 II with a few lenses (including the MASSIVE GX 100-200mm zoom lens), and also, as stated above, two Mamiya AF bodies.
Indeed they are completely different systems that are not comparable. They do completely different things, aside from the obvious 'they both take pictures'. The Mamiya will give you medium format size negatives instead of digital files, and that's about it. The look and feel of medium format and film will be there if you're so eager. The Fujifilm, however, will give you a superb photographic experience as you have tilt and shift in all axes with every lens. Much bigger negative size (almost double), and so much movement. Indeed the drawback is size and weight but again, it is a different kind of experience and is not designed to be carried around (despite the fact that they made a neck strap for it).
Just a few days ago I was taking photos of my first sushi, and I used both my Canon and Mamiya ZD digital back. The Mamiya images were superior to the Canon despite using an L lens, but by the end of the day my thought was "I should have used the Fujifilm GX680 for this shoot. I would have got the shot and look that I was after".
I owned the Mamiya RZ67 system for a while without having used it at all. Only took one polaroid shot and I didn't do a good job at it anyway. It was a long time ago, and I did not even know how long polaroids take to process. That being said, I grabbed it, played with it, messed around with it, attached and detached the many accessories that came with it, and then I shifted it to someone else, and I do not think it is a light weight option. If the Fuji's weight is the ONLY option making you choose the RZ over it, then screw the difference and get a Fujifilm because the RZ's lesser weight will not do you any good. It is still not a carry-around camera.
Alternatively, if you insist on carrying whatever camera around then go for the 645 format (there are also 645 rangefinders, very lightweight, did you consider those?)
The difference between RZ67 and Pro II, I think, is that the latter supports digital backs by default. Some say the older RB is better but only because it is mechanical not electronic, so you don't worry about a flat battery depriving you of shutter speeds, and also it is built stronger and heavier.