It goes without saying that sensor size has a major effect on performance, but when talking about cameras with the same sensor size, in most cases the higher models still have better performing sensors.
It depends on the product/marketing strategy of the camera company. And by "better performing" I mean they use newer or more expensive technology allowing for greater dynamic range, low noise performance. Theoretically, there is no reason a camera company couldn't use the same top-notch sensor in all its cameras of the same sensor size, and make them different only in other features. But this normally isn't the case, as they need to be competitive in the bottom of the market.
For example, Nikon's D7000, its top of the range camera with a DX sized sensor, has a much better sensor than any other camera it offers with the same sensor size. Often it's because a camera company keeps older mid-range cameras (D90) around for longer and they become the new entry-level, or it just uses lower spec sensors (D3100, D5000) on the lower models.
You'll often find that most camera models in a range will use the same or similar sensor, but that there will be one or two models at the top which have a better sensor. In Micro 4/3, virtually every camera available in this format has the same sensor, except for the top of the range Panasonic GH1 and GH2 with a much better performing sensor. Not to mention the $5,000+ (body only) AF100.
As for whether the differences in sensor performance matter, that's up to you. They'll matter less than the way you use your camera, or your skill and experience, or your lenses, or your lighting and choice of subject, and often less than your choice of format (compact, 4/3, DX, FF).