Yes there should be no difference. I believe this is due to how Roku handles account region settings. When you create an account and register your Roku it gets region set to your country at that time. According to what I've read this becomes a permanent account setting, which you can change this by contacting Roku support, but they only allow you to change it once.
A possible workaround is to create a new separate Roku account from your new country and add it to your Roku, however beware this requires factory resetting your device. Also before doing so make sure Amazon Prime is available in your new country.
A possible workaround is to create a new separate Roku account from your new country and add it to your Roku, however beware this requires factory resetting your device. Also before doing so make sure Amazon Prime is available in your new country.