I'm in the same boat, so am glad you've asked the question, so I get to reap the benefits of everyone's opinion. :-)
In my research, I'm really leaning towards the Xbox 360 with Kinect, though there are pros and cons to each. One reason I'm looking into getting a gaming system is to get more active, so I'd want the Wii Fit, Xbox Kinect, or PS3 with Move, and those are all about the same cost, give or take. My husband wants something that the whole family can play (he plays World of Warcraft -- 'nough said), so he's wanting to get some sort of racing game, but that means we have to buy 4 controllers (I think each comes with only 1, or maybe 2), so that would be an extra expense, though I might be able to find some used or "generic".
Wii (Fit) --
Pros: lots of family games; my kids and I have already played it at my sister's house, so we know we like it (though we've recently moved, so we haven't played it much lately); the kids (ages 5&7) don't know that there is any other type of gaming system, so while I'm pretty sure they'd like *any* game system, I *know* they'd like a Wii and be able to play their own MarioKart and stuff.
Cons: you have to use different controllers to play different games (like the little tennis racket to play tennis, a golf club to play golf, the balance board for the exercise game), and that takes up space (we are living in a small space, which makes me loathe to bring anything in that I don't have to); the graphics aren't as good as the other two; you can't expand the system nor play DVDs on it.
PS3 with Move -- (I know the least about this, since my friends recommended we get either the Xbox with Kinect or the Wii, so I haven't researched it as much)
Pros: it can play BluRay discs and stuff, and has great graphics
Cons: none that I know of, except perhaps it, like the Xbox, is geared more towards gamers instead of families, so it might not have as many kid-friendly games
Xbox 360 with Kinect -- (this is the one I'm most leaning toward)
Pros: YOU are the controller for the Kinect/motion games, so you don't have to get anything in addition to having the regular wired/wireless controllers to play games like racing, and I *really* like the idea of not having 50 different types of controllers like you have to have with a Wii to play all the games (ok, exaggerating... a little). This "forces" your whole body to be in motion, and not just your hand with the controller. (My sister said that one time her son was playing a Wii running game, and while he was supposed to be up and running in order to play it, the Wii could only sense the controller/remote that was in his hand, so he was just moving his hand back and forth very fast to imitate running, while he was sitting on the couch. :-/) The graphics are better with this than the Wii; it's expandable (more hard drive space available if you want to upgrade); you can play DVDs in it
Cons: same as PS3, plus you have to pay to connect online