You will notice a decrease in performance on the Series S. It really just depends on how much you are willing to spend. It's hard to say how much of a difference there will be because every game and developer is different. I play MSFS on the Series X but have not tried it on my Series S yet. I would expect a decreased resolution on the Series S or some other measure of decreased performance. Maybe less anti-aliasing? However, the Series S is an unbeatable Gamepass machine for super cheap. As I mentioned below, I got my second Series S for $100 on Facebook Marketplace. Have a look at some YouTube videos that discuss this very topic. Here is a direct graphics comparison for MSFS!
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This video from Digital Foundry also highlights specific differences for MSFS that usually aren't present in other game. The short of it is that you might actually notice more stutters on Series X than Series S, surprisingly, at the quite obvious expense of graphical fidelity.
I have a Series S and do quite enjoy it alongside a PS5, as far as Flight Simulator goes it runs well but it didn't translate well to a controller IMO. It's also not terrible on 4k displays but much better on a 1080p display.
Biggest issue I have with my X is where the heck to put it. The giant pillar design doesn’t blend well with my TV setup.
I'm lazy so I'll just link to my comment on this very thread.
I haven't actually reinstalled MSFS since upgrading from a Series S to a Series X earlier this year, so I can't confirm whether stuttering on the X is still a thing, but performance on the S was pretty much flawless. I didn't install Lost Odyssey on the S back when I had it so I can't tell, sorry!
As for performance and graphical fidelity in other games, it will vary, and you'll likely notice it, as did I, coming from a PS5 - especially on 1440p/4K set. As a game pass machine though, it's really hard to beat price-to-performance wise.