I've owned several Apple TV 3s, a Roku stick, and a Roku 4, plus I've used the Apple TV 4k several times in the Apple store.
The Roku stick completely sucks because it's so slow; we only have it for guests in our spare room.
The Apple TV 4k's UI is much nicer and much faster than the Roku 4's. For example, Netflix starts up much faster on the latest Apple TV than it does on my Roku 4. This is the biggest reason I'm considering moving back to an Apple TV.
Regarding the UI, each Roku app feels like it was developed by a completely separate team that had no idea what other app developers were doing. Even things like the onscreen keyboards are different with some being alphabetical and some being qwerty. With the Apple TV, at least the main apps have a consistent look and feel.
The Roku home screen has (unobtrusive) adds whereas the Apple TV does not. This doesn't bother me that much but I completely understand that lots of people might hate this.
The other obvious thing you get with Apple TV is integration with other Apple devices and iTunes.
Regarding stability, I've never had any problems with any of them outside of having to reset both Apple TVs and Rokus on rare occasions.
If I had to pick one today, I'd buy an Apple TV 4K especially now that Amazon Prime is on it and this is coming from someone who doesn't use iTunes and has never purchased movies from it.
Not trying to disagree with you but Plex fails allot. I actually gave up on Plex because of how much it disconnects and fails so often. Home Share does what I need it to do and never drops off.
I'd say this is a problem on your end and not with Plex. Myself and countless others use Plex on a daily basis and it's rock solid for us. It's very stable no matter if I'm using it at home or watching something remotely. Home Share isn't nearly in the same league as Plex.