The PAL version (= European and Australian version) is based on FFX International, as it has Dark Aeons, Penance and other super-hard extra bosses like that. The US version doesn't have those. Here are some ways to know whether you have the American (not many extra bosses) or the PAL (many extra bosses) version:

1) Without a mod-chip, the American version doesn't work in a PAL PS2 and vice versa.

2) When you begin a new game, you have only one kind of Sphere Grid in the US version. The PAL version asks you whether you want the Normal Grid or an Expert Grid.

3) There's a bonus DVD coming with FFX PAL. It contains interviews with the FFX staff, Suteki Da Ne music video and trailers for Final Fantasy X and Kingdom Hearts.

Hope you'll enjoy FFX if you get it for your birthday.