I've spent about a season and a half on the royales, 20 ish days on the 3.Zeros, and I'm pretty much just going to agree with everything thats been said here. Although in my mind, they are definitely 2 completely different skis.
The royale, although far more versatile than others in the catagory, still skis like a very freestyle oriented ski. In fresh snow, it likes to play around and jump off things. As long as the snow is soft, it can hold its own at speed. When you get into harder crud I found it does bounce around as the tips are still fairly soft despite the stiffer midsection. You can get around on groomers just fine (one of the awesome things about still having a full sidecut) but it doesn't have the hold of a cambered ski.
The 3.Zero, like said above, is fast. The only place I had issues was low speed low incline fresh. Just not enough width/rocker to keep you up when going slow. Easy solution, go fast, ski less flat shit. At speed and/or steeper terrain, no float issues whatsoever. Way better in crud too, as expected (camber, less rocker, decently long running length, again a full sidecut). Feels more like a traditional ski on groomers.
The best way to describe the two skis is that the royale gives you that surfy, bouncy feel while the 3.zero skis more like a traditional ski when not in fresh snow. When I bought the royales originally, I was all "yeah I'm gonna do so many switch landings in pow and 180 all these cliffs BRAH". Now what I'm looking for in a ski has changed. Why ski pow switch when you can ski it forwards and go faster. Why bounce around when I can just straight line it. Now I'm actually on 196 renegades since they work better for me. It came down to those and thirteens, just a better deal on the rens. If I had to make the decision between royales and 3zeros again I would go 3zero.