If you want to look at black and white... sure, but measuring the Axys is in a grey area.
Lets go back to the math first. 5lbs with a KPA, silicone tubing on pump gas isn't 40 hp......period. I know the math, my turbo elementary school as you call it started over 20 years ago.
Then you put a insufficient clutch set up to it and your getting even less to the ground. Then add on top of that a insufficient shock set up, and you have a sled that wont get out of its way no matter how much hp you add to it. You can add 14 lbs of boost, and it will still be a turd.
Then enter the grey area as I called it of the Axys, This sled was designed to be on edge and in the trees. Just like the pro's ride it. If you want to compare on a open hard pack flat, sure the turbo will win and run circles around it. Put them in the steep, tight trees. That's what the Axys was designed for. Put a stock 850, with proper shock and clutch set up, compared to the half azz turbo. The same rider will ride better and be faster on the 850.
Someday you will understand its not always about the math and HP numbers. Like I said before good luck.... maybe someday we will run into you on the mnt. and we can discuss it.
First things first, no doubt stock sleds are amazing these days. They absolutely have their place and with a capable rider can go just about anywhere.
That said an Axys is probably the most user friendly 2 stroke turbo going. There are countless clutch setups to pick from, the skid doesn't need much to be setup for boost (stiffer RTS spring and valving), the static weight distribution makes the sled ride really well even at slow speed with minimal transfer and the 800 CFI with a turbo build power really really well. There isn't much of a learning curve to riding one (especially a low boost setup).
A turbo'd Axys is *the* most capable tree sled in the world, especially when things get deep. Literally every single Polaris pro has one. Why? Cause they rock! They are fun! They are incredibly capable! They are more capable than their stock 800 (and now 850!). Every pro I'm buds with rides their stocker at a 1/5 ratio, if that, compared to their boosted sled. So tell me again how my "grey area" math is wrong? If anything Polaris would prefer they ride their stocker more.
We can debate actual horsepower all you want, but I promise a sled with a good map running 5psi will outclimb, outperform and generally be a more capable sled, all other things being equal, *especially* when things get technical. Again, not saying a turbo is for everyone, but that's not the point of this thread. Just like in the car world, some people love the super linear power delivery of an NA engine. Some people love the pop of a turbo. Both require their own style! We are talking about what is most capable, and what is the best bang for the buck - I realize I got off topic!
No doubt I'd take a boosted 800 with nothing but a little clutch refinement over a stock 850. There are other chassis this can be a harder decision, as they aren't out-of-the-crate as easy to setup for boost (ski-doo - awful skid). In this case, I don't think its a very difficult decision if you are looking for straight up performance.