I own two of these (Whiteout and AX) and have demoed the AR in different years. The AX is looser, the Ar is more precise, and the White Out is in between but different: it has a big, wide almost spatula tip. That tip handles crud and soft snow, including in bumps, much better than a ski with that narrow a waist might. The Whiteout is also really great at body separation, fall line carving turns - the body still in the fall line and from the hips down doing the carving. It's a cheater at doing such turns.
To me, the AR is a bit too precise for easy bumping, though for carved bumping I found it swell.
And now, another "Groundhog Day" like return, I'm afraid.
(Sorry, apologies to the Popular Wisdom here, but....) I have a possibly contrarian view on the AX lengths myself. For an expert or well advanced skier of average size who likes to charge on edge at times, and skis less in steep mogul fields, or moguls in tight trees, please try the AX 182/183 before you buy. I and others prefer it, by a lot.
The AX 175 is looser when wanted, precise when wanted, admittedly better in bumps; but with a problem: its rebound doesn't quite fit its carve/flex, so that whole process is telescoped, so to speak, into a shorter space or time - quicker. An extra boost. Very fun though. (I believe a similar description of the 175 AX was given in an earlier thread by the Stöckli rep himself, by the way - except he said it better, as I recall, and more thoroughly.)
The AX 182/183s are a different critter. My 183 is maybe my favorite ski, or close (for me, moved forward on demo bindings to +2 cm. or +2.5 or even +3 cm.), while my 175 (on the line or close) is not, fine ski that it is.
If you want to take the AX into steep, uniform bump fields regularly, and ditto with steep, tight, moguled up trees a few days after the storm, then get the 175.
But if you like to freeride on edge, fast or medium, relaxed or driving, ride the rails on mild and/or non-uniform bump fields and relatively unbumped up steeps, in addition to groomers, then the 183 is tops, for some (including both me and my favorite skiing buddy, both of us on matching 183s, though with different bindings and fore/aft mount points).
Many people say get the 175 still, because it retains most of the stability of the longer ski, with more versatility. Yes, but it loses the amazing smoothness, and the dialed in stable ride with that, and the way the ski's carve is synched with its flex and with its rebound so well.
Some also say a really heavy/big/powerful guy may be needed for the 182/183. But I'm only 150 lbs/5'10" and still old on a good day (though my AX buddy is c. 185 lbs/5'9" and younger, moved forward on his only +1 to +2 at most maybe). So clearly on the smaller, finesse side works too.
Finally, if you are a charger now and then (and also have the mentioned preferences in terrain), the 183 is up there with the very best charger skis on up to 3-4" at least of powder. (While for me, the Whiteout is good for 6" or so, with lots of crud.)
And, man, is the AX great on the one or two slope early and late season days: two of my first four were on it.