The Apple TV remote is way more useable, and HDMI CEC just works™, which never ever was true with the NUC. I really like the client-server model - the Apple TV is my dumb front end for Plex, Steam Link, and so on. It also is well supported by every streaming service.
All of the Apple TV apps are designed with a UI for a TV and remote, not a user sitting two feet from a computer with a keyboard and mouse, and are way easier to use sitting on a sofa then a keyboard + browser combo.
I could fiddle with the NUC and make it work, but it was not family friendly. In general, the "it just works" factor is extremely high, which I could not say for the NUC.
If Apple ever goes evil, I'll just switch to whatever the best solution is when that happens (maybe a rooted Android TV device?). It's not like I'm marrying it. An Apple TV is $150. I've gotten 4 years out of my current one. The cost is negligible.
As I've gotten older, I've really come to value the "it just works" factor. I don't have time or energy for fiddly stuff anymore. After I put in the time to set something up, I want it to be rock solid. To each their own though.
Which wireless keyboard do you use? I've pretty much exact same setup - TV + Linux Mint + Logitech K400+. I'm just looking to see if there are better options for K400+
The keymap takes some getting used to.
An Apple TV is probably also OK, but likely also much more expensive. Also, Apple is a company that is and always has done all they could to lock down their platforms, lock in their users and seek exorbitant fees from developers releasing to their platform.