It seems as those there's a swell of interest in robot vacuums, so even though this is a fan/expert site, I'll start with something for newcomers: none of these things are a match for a neatnik armed with a first-rate regular vacuum. The main reason people like me claim that our floors are cleaner than they've ever been is because robots don't mind repetition; it was just as easy to make my robot clean the floors three or more times a week, whereas before I'd put the task off for weeks, until things had gotten disgusting. And robot vacuums don't clean stairs or windowsills or anything off the floor. Robots are for people who hate vacuuming and like gadgets.
With that out of the way, here's my story. I got my first Roomba, a 400-series, several years ago and became enamored of it. But it broke down a lot. I've got a teenager and a dog, the dust and hair would get worked up inside the thing, and eventually it would die. After three years, I now have one sort-of-working Roomba and -- I kid you not -- four Roomba carcasses stacked up in the basement. (The company has a generous replacement policy; I paid only for two.) I eventually learned that you can make the Roombas last longer by cleaning them obsessively with compressed air after each use, but this was a pain in the neck and made its own mess, what with all the dust blowing around. The reason I jumped on a deal for a Neato ($300 at Woot) is that I hoped it would be more durable and require less maintenance.
And so after a little experience with the Neato, here's the comparison between the two. The only way the basic Roomba knows there's a wall or a piece of furniture is to bang into it. Its core algorithm seems to be "when X happens, choose randomly from the following several behaviors." It bumps into a wall, and sometimes it goes right, sometimes left, and sometimes turns around. It goes under a chair, it bangs around between the chair legs trying this and trying that until it finally emerges and trundles on. It has the brains of a scallop. It relies on randomness instead of smarts to cover its territory. This is not necessarily a bad thing; all that randomness can work to get a room nice and clean. (Repetition is good, remember?)
It also has a "dirt detector" so that when it encounters an unusually dirty spot (say, in front of an outside door) it goes round a few times to get it all up. And it has a both a rotating rubber beater and a rotating brush, which together do a decent job of shaking the dirt loose (but which also generate a cloud of dust that gets up inside the machine).
The Neato, in spite of its dorky name, is certainly cleverer. (Clever isn't always better; the cleverest kid in my high school almost blew himself up trying to make nitroglycerine.) What it does is use its laser guidance system to map out a room into quadrants and then does a back and forth motion to cover the territory in an orderly fashion. It indeed does a better job of finding its way from room to room in my small house, it finds its way back to its base much more often than the Roomba, and gets stuck a little less often. I'm finding I can set it to work automatically when I'm not around and so far it's almost always cleaned the entire first floor and returned to base when I return; doing that with the Roomba wasn't worth it because it more often than not got stuck somewhere or ran out of juice, so I just ran the Roomba in one room at a time while I was at home doing other things. For me, less supervision means more use, and thus cleaner floors.
But the Neato has its faults. In its effort to avoid obstacles it more often misses spots by steering around them (edges and corners especially). In my cluttered little house it sometimes maps its quadrants so small and overlapping that it effectively covers the same spots many times, becoming more Roomba-like in its behavior. It's completely bewildered by the black wrought iron legs of my coffee table. (I fixed that by covering them with masking tape, but that's not a great solution, to say the least.) And its laser "eyes" are strangely mounted towards the back, so that it can't see things shorter than it; I have to pick up the dog toys or it will try to drive over them, which hangs it up, wheels in the air at a crazy angle. Ultimately, the Neato is less like a scallop and more like a four month old golden retriever puppy; it goes off eagerly on its mission, but gets easily distracted and sometimes trips over its own legs.
For my purposes, it's important that the Neato's single rubber/squeegee type rotor underneath does not get so tangled with dog hair, its design is much easier to clean and seems to need less maintenance, and the machine mostly makes up for it's lack of a second brush with a stronger vacuum. It still does a lot of seemingly random banging around in my small cluttered house. (Its virtues may really shine in a large McMansion with vast tracts of open space.) And on a tightly woven carpet, the Roomba was slightly better at scooping up the dog hair because of its brush. But as long as it keeps running, I'm willing to use my dust buster to get at edges the Neato missed, which I'm hoping will be longer than the Roombas did.
There's a lot of action with robot vacuums right now. New expensive fancy ones like the LG Hom-Bot are becoming available, the Roomba makers have outsourced some smarts to little "lighthouses" that try to guide the robots from room to room, the more expensive Roomba 700-series is intended to be more durable, and there's a high-priced version of the Neato so far available only in Germany that has a better brush and other neat features. If these souped-up ones come down in price to the range of an ordinary vacuum cleaner and get to the point where they can last more than a year, they may become quite widely adopted. Until then, I'll tentatively recommend the Neato.
[Update, two months later: so I've already had to use the warranty due to an RPS error -- they shipped me a new one, no questions asked -- and the hope for better durability than the roomba is not looking so great right now. It looks like you really have to treat these almost like rental items, and assume that once out of warranty, you'll have to throw them away before long. But in my particular house, once I'd learned to take care of a few trouble spots, the Neato vacuums the entire first floor every time while I'm away, almost never getting stuck or running into problems. And it involves much less maintenance than the roomba 400-series. I pretty much just set the timer and empty the bin now and then, and don't have to think about it hardly at all. So ymmv, but for me, the Neato is quite a step up from the roomba.]