I don't want to make your decision harder, but have you considered a Rainbow? It uses water to capture everything you vacuum up, so it can't get back out into the air. It seems like there is one other brand out there that does that.
My parents had a Rainbow when I was growing up, and when my husband and I were first married of course we couldn't afford one. We got one a couple years before our son was born. Day care lady has one, too. Everyone I know who has one is so surprised at all the stuff it sucks up. It is yucky to dispose of the water and clumps of hair/dust (we have a cat), but I feel it has helped with allergies and overall to have a clean home. There is a stairway attachment that is great for stairs, and other attachments as well.
As for the two brands you mentioned, I know a couple people with a Dyson. They like them, but one of them had a Rainbow demo and it got stuff out of her carpet even though she had just vacuumed with the Dyson. Still, the Dyson is less money than a Rainbow, so out of the two options you listed I would choose the Dyson.