It's already been confirmed that the ways in which Series S and Series X handle Xbox One titles varies. Only the Series X will benefit from Xbox One X enhancements to existing games - which typically boils down to resolution boosts, higher quality textures and other graphics-driven effects. Xbox Series S brings its additional horsepower to bear in improving the experience of Xbox One S titles instead. This is more limiting in some respects (a game hard-coded to run at 900p will not run any higher on Series S, for example) but the new console benefits from increased resolutions in games that use dynamic resolution scaling, as well as improvements to texture filtering quality. Obviously, running games from solid state storage reduces loading times significantly, while the Auto HDR feature we've seen running on Series X also features on Series S - all games should present nicely on HDR screens, whether they natively support high dynamic range or not.
So yes, Xbox One games do run better on Series S. Where frame rates are unlocked, they will be higher. Where dynamic resolution scaling is used, resolution will be higher. There will be better texture filtering. And dynamic HDR will be applied. But nowhere do they even hint that Xbox One games will be running at a resolution higher than 1080p. Yet for Xbox and Xbox 360 games, they explicitly state that this is the case; titles from those generations
will be rendered at resolutions up to 1440p.
I'm pretty sure one of the BC videos from yesterday showed off a non-enhanced title on Series X running at 1080p. I can't remember which now though. Might have been Jeff Grubb's?
FYI, I'm not hating on Series S. I've got one on order. But it's worth being clear about what it is and what it isn't. It is going to enhance old games. But for the ~750 Xbox One Enhanced titles, the Series X is going to be markedly better (mostly; not all of the "Enhanced" titles are very "enhanced" at all).