I have a memory card from a 360 arcade and just done a test with my FF. You can save progress on it.

That said, I am not sure I would buy any console without a HD. There is simply to much DLC coming out, you would miss out quite a bit over time.

My gaming is done on a 360 and PC and have just got a second hand PS2 so I can play some earlier FF.

There is no doubt the game looks better on a PS3, but it still looks really great on a 360 - best graphics I have ever seen in a game.