I have a US and a EU account. I use mobile authenticator on EU but I cannot attatch it to US account (only one account per authenticator).
Therefore I have to use a physical authenticator for the US account.
The problems that occur:
* I have to type an authenticator code EVERY time I switch accounts.
* I must always remember to bring the physical authenticator if I am to play at different places (I have 3 places for gaming).