Maybe, maybe not. HDR doesn’t always do the same thing on every scene. If the range of light in a given scene is within the both sensor’s native range, HDR will do nothing on either phone and you will of course see no difference due to HDR. If the light values are out of native range of the X sensor but within the HDR range of the X, they’ll likely also both look the same due to HDR.
So you’ll have to have a scene that exceeds the X’s HDR range but is within the XS’ HDR range. Then you’ll see a difference.