Each of the three characters do play through the same dungeon areas, though since the skill-sets differ from one character to the next, different approaches are often needed to overcome the same obstacle. As an example, remember the Devil's Corridor from Ys I? It's back in Ys Origin, and if you're playing as Hugo, you can get through it exactly the same way you did in Ys I. But if you're playing as Yunica, the solution is a bit more obscure -- and if you're playing as The Claw, it's COMPLETELY different, and much more intense. So it's certainly not the exact same experience from one character to another... but admittedly, it is fairly similar, and you are expected to play through the entire game with each character in order to get the true ending. I'd recommend playing through with one character, then playing a different game, and coming back later to play as the next character. Leave some time between playthroughs, and the dungeons will never seem old or repetitive.
Regarding 360 controllers, the game does not natively support them, but as long as you have the right drivers installed, you'll still be able to use them. Button config is a breeze, and can be done in a few seconds prior to starting the game -- the hardest part is just finding the right drivers for your computer, which also shouldn't be too big a deal.
And Chelli: Each character has his/her own story. Once you've chosen a character, you can't switch mid-game -- you're playing as that character through to the end. And while the basic storyline of the game is the same in all three scenarios, each character "remembers" it differently, so the individual events that occur within the tower vary quite drastically -- even to the point where certain characters who live in one scenario will die in another, and vice versa.