I don't have stake in either of these devices however a few of the apps were "further along" with the XS Max. Youtube was already autoplaying videos on the XS. Similar with tweetbots state. Appears the XS was doing better on the network overall, but because of that perceived performance can be effected since loading a video that is about to autoplay can effect load times of the rest of the app.
The screen resolution itself doesn't effect performance (battery not withstanding) however scaling will. The iPhone XS Max and XR use different scaling, x3 and x2 respectively. This is akin to rending a 1080p image on a computer, the computer performance is the same whether there is a 1080p monitor hooked up, a 4k monitor hooked up or even no monitor at all. This is why even though XS has ~22-23% more pixels its not 22-23% slower.
Apps cache assets dependent on usage. A fresh boot doesn't remove this data (app name/library/caches). The difference in what is cached and what is being loaded/rendered/scaled/etc makes a performance difference.
I feel the XS Max looked faster to me as it was getting more accomplished however I think that was because the XR network wasn't functioning as well. Now if that wasn't a fluke due to that specific wifi then the XS Max is faster (App Store wouldn't even load in a timely fashion on the XR) however I don't think that was the case.....