M&P Shield or an XDS?
Can’t comment on how the M&P Shield shoots, but the one I dry-fired seems to have the same overall feel, super ergonomics and the same great in-hand feel as the M&P 45 I have with a 4.5” barrel. The darn thing just feels like it was made for my hand. M&P’s are a great pistol; just wish S&W would smooth out that rough trigger feel (I’m going to go for a trigger mod for mine very soon).
As far as the XDS; I own one as well, and it’s a very nice pistol. For such a small frame & 3.3” barrel, the recoil from the 45acp is very controllable. At 15 yards, grouping was amazingly good, and I’m no professional. With the XDS 45acp's relatively small & narrow frame and a traditional single-stack 5 round mag, it may be a nice concealable pocket pistol, but your pinky finger will fall on the underside of the mag if your hand is larger like mine. If you opt for a XDS, buy an optional 7-round extended mag which comes with the grip extension.
Also, I’m not aware the XDS platform is yet available in a 9mm. My wife has the XD sub-compact 9mm model which has a 3” barrel. It is a completely different gun than the XDS. Although the XD sub-compact's barrel is smaller in length, the pistol is larger overall than the XDS 45acp. The XD sub-compact has the higher capacity double-stack mag like the other XD line, and has a wider frame and generally a bigger overall profile than the XDS. The wife likes her XD sub-compact; it shoots very smooth & accurate, not to mention the cost of 9mm ammo vs. 45acp. This is the pistol which is a comparable size to the M&P Shield.
I believe you'll find the light strike & other problems you may hear about on the higher-end, smaller frame pistols is from cheap and / or defective ammo being used, limp-wrist and / or soft-grip handling by the shooter- not the pistol's themselves. (As compared to a friend who has a Beretta Nano 9mm and who went with my wife and I to a tactical defense training class, and that’s all that pistol did was jam & misfire.) The S&W M&P's and SA's XD / XDS on the other hand are all very well made in my opinion, and we have had no such reliability issues whatsoever with any of ours from either manufacturer. Just keep 'em clean, hold on and shoot a better grade ammo. Use the self-defense nylon tipped or hollow point ammo, and I’m sure the 9mm will do the job. If you’re considering 40cal; with ammo cost & recoil all considered, you may as well go for the big-guy 45acp in my opinion.
As far as your budget, you’re not going to find the XDS for $500 out-the-door (maybe a XD subcompact alone without the accessories kit). The Shield I believe is however in that price range. If you like the M&P's ergonomics, trigger feel and the budget is $500, go with the Shield (not to mention the M&P is an all-USA manufacture, where the XD & XDS’ are manufactured mostly in Croatia- albeit a region of the world that makes some fine guns).
My general recommendation however is before you buy, take the time & find a dealer who has some demos / rentals and spend $50-$75 on some ammo, range time and / or rental fees. Shoot any of the M&P and XD line of pistols they may have; go with your gut feeling of which manufacturer’s engineering feels best for you and then place your order & buy! Good luck, and great news about Illinois maybe passing a CCW law.