Some of the answer to this would depend on Internet performance at the two locations.
But, assuming both have good upload and download speeds, I'd suggest trying the NAS in the EU to begin with, and setup Tailscale with an exit node in the US. This should be relatively easy to setup and test, and you can always move the NAS later to the US if you decide it would benefit from being there performance-wise.
I'm actually doing the latter now, as I'm based in Portugal for the Winter with my servers and Tailscale exit node in the US. This works very, very well as long as you have high confidence in 24x7 operation of a remote server. I have that, including an orchestrated multi-UPS system for orderly shutdowns and startups in the event of a power interruption or other issue.
Since an exit node is more bulletproof as a totally remote entity, I think you'd be best off keeping the NAS close at hand, in the interest of being able to deal with any issues that require hands-on. I've experimented some with different exit nodes, and I'd suggest a RaspberryPi4 or better at minimum. I'm currently using a dedicated Proxmox LXC container for mine, which is slightly faster in my case than an RPi4.
I would not recommend using a Windows PC, router, Android device or earlier RPi for an exit node as the performance would likely be disappointing.
EDIT: Probably worth adding here that the ultimate would be to have a Channels DVR server in both locations. That way you could share channels in both directions, using an M3U generated from one as a Custom Channels source in the other. Exit nodes on both ends, and you could have your "on ramp" to the Internet where it works best for you from anywhere in the world.