I have made anew character at the NA server, after having played on the EU server for almost a year. All the rewards popped up right over there, as expected.
The only thing you need to do is download the 35+ GB data, install that and if you use Add-Ons, copy those over from the NA server's directory (default C:\Users\{your account}\Documents\Elder Scrolls Online\live\AddOns\) to the AddOns directory of the EU server (default C:\Users\{your account}\Documents\Elder Scrolls Online\liveeu\AddOns\).
I have made anew character at the NA server, after having played on the EU server for almost a year. All the rewards popped up right over there, as expected.
The only thing you need to do is download the 35+ GB data, install that and if you use Add-Ons, copy those over from the NA server's directory (default C:\Users\{your account}\Documents\Elder Scrolls Online\live\AddOns\) to the AddOns directory of the EU server (default C:\Users\{your account}\Documents\Elder Scrolls Online\liveeu\AddOns\).
With a 200 Mbit connection and an free quota on the ISP, we don't mind downloading it all again. At next patch day it's downloading all that again anyway. EU, NA and PTS, on 3 PCs. In the end it doesn't matter, we still have the Manifest Errors. :PAll you need to do is copy your EU data to the NA folder, delete the 3 mentions of Version in there and run a repair on logging in to NA.
No need to download an additional 35+ gigs.