This article simply explain the difference between RISK - Factions and RISK - The Game of Global Domination games:
I just went ahead and bought Factions after I found out about it. Has new gameplay modes, and such but still includes the classic game if you want it. Gamepad controls, story and online play.
Factions is indeed the best option. I was wondering just about the other two "vanilla" versions.
The newer one I guess, it looks nicer and it's cheaper. It looks closer to the actual board game. Online matchmaking will eventually be added to it.
The old vanilla Risk only has local hotseat multiplayer as far as I know.