I have had a Huben for a few years, so I have that as my benchmark in terms of what I am used to. I picked up a Sidewinder a few months back, so I can compare and contrast them. Both are in .22 caliber.
The Huben has better build quality, a much better trigger, is quieter both in terms of muzzle sound (especially with an added moderator) and mechanical sounds on the shot, more usable range of regulator adjustment (and thus air charge), has a more positive feeling and better protected power adjustment wheel, and is ambidextrous (the Sidewinder would be almost hazardous for lefties).
The Sidewinder has the convenience of the removable mags, a barrel that is much easier to remove for cleaning or such (the Huben requires more disassembly and degassing to do this), the added safety next to the trigger (I really wish the Huben had this, as you have to take the gun off your shoulder to operate the safety), is a little lighter, and of course has the full auto function.
The Sidewinder has a tensioned barrel via the CF shroud, while the Huben does not - but the Huben shroud is baffled and leads to a much quieter gun (the Sidewinder's shroud is not that effective, as it really does not have a great stripper and has no baffles). I did buy the adaptor for the Sidewinder, and currently run a Huma 40 Compact on it, and that made it much quieter than stock but it still needs more suppression (but even with more will it still be louder than the Huben as the action is louder).
They both have tons of power, easy adjustment, and are really impressive air guns. If you only have one, and never get to shoot the other, you'd most likely love either one. For me having both, if I could only have one for my needs it would be the Huben, mostly due to the trigger - if the triggers were equal it would be a harder choice, but for me the edge would still go to the Huben as it is more backyard friendly. But then again, that full auto is a ton of fun (if not really all that useful in practice . . . ). Additionally, I don't go to ranges (at least to date), but if I did the ability to easily prove the Sidewinder safe by removing the magazine would make a strong point in its favor.
Edited to add one key thing - parts and support. I have seen nothing on this on the Sidewinder, other than AoA servicing them. No parts diagram yet or anything on the Sidewinder. The Huben has full support, parts diagrams, and all parts are available for purchase for any DIY repairs when possible, or even to have on hand if needed. If that matters to you - I'm sure AoA will be able to service the Sidewinder for a long time, but doing it on your own may never be an option . . .