I have had 3 roombas and now have the XV-11. Amazing difference. Roomba is only a brush. Like a carpet sweeper. This thing has 2 motors. One to "drive" it and one to run a vacuum. Yes, a real vacuum that pulls suction. It pushes the air through a filter like any other vacuum. I was amazed the first use (and still am) as to how much dust this thing picks up. Very clean floors. Pulls dirt out of the spaces between tiles in the kitchen where the grout is lower.
Second, it does, as others have said, map the room. Then goes around it twice on the perimeter, then vacuums it in the middle in back and forth passes. When I set it at bedtime, in the morning, the whole first floor is marked with those cool "just vacuumed" lines. Just looks cleaner that way! Oh, and I discovered that it will just change the direction it vacuums from north/south to east/west and even has done diagonal a couple times. Amazing. And better overall coverage.
Also, it will vacuum an entire room, then go through the door and do the next room. In my case, it thinks that the couch and chair are close enough to make the family room a separate room from the kitchen. So it does the first room, then the next, then on to the dining room, then the living room. Mapping each one.
If it runs out of power, it shuts off the vacuum and powers back to the charging base. It's weird, cause it's very quiet when it's just moving and not vacuuming. After it charges, it starts up again and goes back to the exact spot it left off and finishes the entire floor of the house. The startup can be really startling the first time!
Also, the upgrade of firmware made it dock better, kind of wiggling it's butt until it's happy with the connection. :-)
It handles weird changes in terrain really well, as the base of "my" chair is a flat circular wooden base, and it goes up and down and around it with no issues. It does climb up onto the base easily, instead of bumping off it like Roomba.
I love this thing. Bought mine from Hammacher and Schlemmer because of their lifetime warranty program, not trusting that it would be really long-lasting. But I've had it a year (or more?) and it's no issues. Clean the beater bar and bearings once a month or so and it's happy!
I spent a lot more, and STILL think it was worth it. This price is very good.
Hope that helps!