Maybe the Z Avenger SS is more like the Sidewinder, but in general, I find the Avenger SS is noticeably more understable than a Champ or Star Sidewinder. When brand new, the Z Avenger SS will have some minimal fade on the end of the flight, but usually you won't ever see fade on it unless it stalls. The Sidewinder has more fade to it, but not that much.
In terms of overall stability, I find the Avenger SS in all plastics to be closer to the Roardrunner than the Sidewinder, but I don't feel like the Avenger SS is quite as fast as either of those discs, nor flies exactly like either. It's still the same type of disc. If you are looking for less overlap, having 2 of these three discs in your bag (avenger ss, sidewinder, roadrunner) at the same time, would probably not be great. I know there's plenty of ppl that like to carry both the sidewinder and roadrunner in their bag at the same time, but adding an Avenger SS to either of those discs makes less sense.
I use the Avenger SS primarily for rollers, turnovers, annies, and low powered straight shots in the woods. It's a fun disc, but I replaced it with a beat X Avenger, which is a little more versitale for me, and probably is closer to the Sidewinder when broken in the Avenger SS is.
I've never really been a fan of the FLX Avenger SS, because it doesn't roll well, which defeats half the purpose of the disc for me. If you don't like to use the Avenger SS for rolling, and you want something that is slightly more stable than the ESP Avenger SS out of the box, then the FLX Avenger SS isn't a bad choice. But, they will still break in, to the point where they are basically an ESP Avenger SS that's more grippy, but can't roll for crap.
I'll second what someone else said about max weight red Z Avenger SS's, they seem to be the most consistently stable of the mold that I have seen, though the Cryztal Z's can be that way too, but are harder to find, easy to lose, and typcially cost a few bucks more.