I've done both- enclosed box w/ floor and wire cage.
With the wire cage, you're going to need more heat, because the wire holds absolutely nothing in. I brooded my chicks in a wire cage in a tack room in a CA spring, so heat wasn't that big a deal. You're also going to need a place where they can rest their feet from the wire (a piece of plywood, etc for them to walk on) or they can end up with wicked foot problems, which kind of defeats the purpose of the wire floor. You could also end up with sick chickens later on, as they get no gradual introduction to cocci and other bacteria from the litter- they just go from wire to whatever will be in their coop, and that sudden of an introduction to a bacterial load can mean bad things. On the upside, they're much easier to clean, and you're not spending money on bedding (yet).
The brooder box with the floor is the way I go these days. It's more "natural" for them, gives them the chance to build up immunity, and the box holds in heat, which is a good thing, as I now live in VT. It is more difficult to keep clean, but by more difficult, I mean I have to scrape out bedding, then haul it outside, hose it out, and apply a scrub brush and bleach solution, as opposed to just hauling it outside and scrubbing it out. Not that much more effort, really.
