Just came from the store, I tried the 11 Pro, 11 Pro Max and the 11. I noticed that the 11 Pro and Pro Max stutter quite a bit, more so than the 11, which stuttered only a little. It was odd to see this, particularly since the stuttering was somewhat different than on my XR, in that when you tap on an icon on the home screen, it takes a moment to register the tap and open the app, after which there is a mild stutter in the animation. It was surprising to see this as previously when I tried the XS Max (after launch) and the 11 Pro Max (months ago), there were no stutters, the phones were smoother and faster. All three phones were on 13.3.1., max brightness, wi-fi on.
I don't know if it's the demo mode affecting this, but I did expect these three phones to be smoother than my XR. Not perfect, but smoother nonetheless, and they aren't. It seemed to me that the 11 Pro Max stuttered the most.
Also checked the storage, naturally these units are packed with apps so that customers can try them out, but none of these had less than 20GB of storage available and they were 64GB models, so it can't be insufficient storage. Also tried the app switcher, there were just a few apps on there, so it's not like the phones were used too much. It seems to me that it's down to iOS 13 being poorly optimised in this regard and it won't be fixed by users, only by Apple and probably in later versions of iOS 13 or more likely in iOS 14 if it's a stability update.