I had a 2012 Pro RMK then went to a 2015 T3 Summit, now I ride a 2016 Axys. I Enjoyed the Summit but when I got into technical situations I just didn't feel confident with it. It would occasionally do weird, unpredictable things. It was playful and fun in the more open, mellow areas and had no problems picking the skis up when I wanted it to. I thought the front end liked to dive a bit too when I'd let off the throttle in deeper snow.
I prefer the handling of the Axys, it's just so much more predictable and easy to ride. I have had some little electrical quirks but no major issues with it. My little 155"x2.6" did pretty well on a couple 3-4 foot deep days. I was worried I'd miss the 163"x3" but I have been happy with the smaller track. My one complaint is that the 800 Polaris doesn't have the power that the Doo 800 did, and it's no competition compared to the Doo 850.
I have never understood why people think the Doo rides lighter, I disagree. Mine would dive if you let off the throttle in soft snow, and my girlfriend's Expert is VERY planted and feels heavy unless you're pinned. I've tried a bunch of suspension adjustments and it doesn't make much of a difference. Stupid torsion springs. As I write this I realize that it could have fatboy springs in it (her dad ordered it for himself originally then gave it to her), I'll have to check.....
In my riding groups it seems that the older guys prefer the Ski-Doos, and the younger crowd is Polaris, with the exception of my girlfriend on the Expert.
I'm not brand loyal, this is just what I've experienced with the two. If you care about Cat, I think the Alpha is a really fun sled. You have to be careful keeping the track cool and out of the rocks(really any track nowadays), and the front end is a little divey at times too, but it's overall a very playful sled and that track blows everything else out of the water in terms of traction and flotation. I almost bought one instead of the Axys.
I do plan to Snowcheck a new sled next spring for the 2023 model year and I really don't know what I'll order since Doo will likely have a new chassis next year and maybe Cat will surprise us with something new and exciting. I'd need a good test ride to buy a new Doo or Cat chassis, but I'd be confident with a Matryx without riding it first (since there were no geometry changes).