Dyson, hands down. My husband grew up in a big house (with cats and carpet) in England, and his family had a Dyson to keep it clean for nearly a decade. His mom highly recommended it, and even though they're not big spenders, I never thought I would spend hundreds of dollars on a vacuum myself. But I finally caved in, sort of, when I got a major price cut on a new Dyson (~$150 in gift certificates and a 10% discount for starting a new account at Macy's).
This vacuum has been gentle yet effective on cat fur stuck on the blades of greasy ceiling fans, cobwebs drooping from ornate tin ceilings, stuff on the bottom of mattresses, our handwoven rugs, a/v equipment and laptop keyboards, dried exoskeletons of moths or other critters in the crevices of window sills and in lighting fixtures, and oh yeah, hardwood floors and carpets! Amazing how much it picks up stuff that I wouldn't even know was lurking, despite a no-shoes policy at home.
Since using the Dyson for the past 4+ years, I am convinced that my other vacuums were a waste of time and money. The deceptively lower price tags for those machines were actually a false economy because I'd have to pay special prices to get special bags, pay for special maintenance, special replacement parts, etc. If price is the bottom-line deciding factor, you'd be saving a lot more money if you beat your rugs outside with a stick, or get rid of all carpeting and use a Swiffer! ***Just make sure you clean the filter every now and then.