I've been on Polaris since 2012... have loved it. I don't think its even a contest of which sled is the most predictable and capable when things REALLY get nasty. The Polaris just flat works, and like Boorant says, that sled really does become an extension of your body. If you are capable they will take you through some insanely steep tight chit. Our group has had excellent luck with Polaris... knock on wood, we have NEVER towed one of our Polaris' out, and we've probably owned 30+ in our group over the last 7-8 years. Most of us don't run them over 1500 miles. If you are into tinkering, modding, and maintenance the Poo is by far the easiest to work on. They are built smart.
I rode an expert a couple weeks ago. It was awesome. Big time fun factor. They feel/ride extremely light, and hook up like crazy. The bottom end is night and day better than on the 850 Patriot. If a guy is not big into technical tree riding I think its the sled to have. SHOT is BIG PLUS. I have never had a sled with estart, and I don't really mind pulling the rope, but I would get SHOT no questions asked if I bought a Doo. The worst part about Doo is that they suck big time to work on. Things that are SO simple on the Polaris like changing and a arm or TRACK, or pulling the secondary, are WAY more work on the Doo, and that's frustrating, especially if you end up needing to do repairs on the mountain or in the trailer.
Both are great sleds, but they ride completely different. Best thing you could do is ride both... even riding an Axys 800 and a pre Expert Gen 4 will give you a pretty good idea of which model you will prefer.