I'm not sure the cordless Dyson I have compares well to a good corded vacuum cleaner for cleaning power. But for me, I got one a couple of years ago (after thinking about getting a Roomba for the umpteenth time and concluding it wasn't for me) and it's been perfect for my use case. I normally have a housekeeper come by once a month. But the high traffic areas including the kitchen really need a quick vacuum now and then in between cleanings and the Dyson's been perfect for that. I hated having to haul my corded vacuum out to do this. (So I mostly didn't.) Now it's literally a couple minutes work to grab the Dyson and give a quick cleanup.
Same experience for us. The cordless Dyson is a lesser vacuum cleaner compared to our old corded hoover. But it's light, it's easy to grab from the charger and you don't have to deal with a cord, so it gets used more. It just removes all the friction from the chore.
Yeah, the gtech was a battery vacuum too, but placed the motor/impeller right next to the entrance of the device, no long pole. I wanted to love the Dyson because of what we paid for it, but I left me a bit meh. My folks have a corded Dyson now and it is a good machine, but I really feel the shark just wins. Man I am dull :p
My cordless Dyson (V10 Animal, I think) is strong enough to get stuck to the carpet on the highest power setting. I won't use it past medium because I'm afraid that it will tear up the carpet.