"It is possible to play with the same account on both Windows and PlayStation 3 platforms. Customers who own a copy of FFXIV for Windows and wish to use their account on the PlayStation 3 version will need to purchase a copy of the PlayStation 3 version. It will then be possible to use your characters on either platform by tying your existing service account to the PlayStation 3 version upon launching it for the first time. Similarly, customers who own a copy of FFXIV for PlayStation 3 and wish to use their account on the Windows version will need to purchase a copy of the Windows version. However, please note that your account will only be able to log into one platform at a time."

Also... once a PSN account is bound to an SE account, it cant be bound to another one

so yeah.. it is cross-platform.. as long as you have a version for both platforms