In one sense of course the two are literal opposites, but practically they are more like siblings... or perhaps even the same field altogether (though I suspect rural sociologists would reject being nested under urban studies or something. Truth is, sensibly or not, some of the rural stuff does feel like a different discourse - while I think of myself as fairly well versed in urban sociology literature, I'm always a little worried there might be a bunch going on over there in rural sociology (over where?) that I don't have a grasp on. (In this way it's a bit like geography or urban planning, other fields with which I'm quite familiar and even overlap with, but still not as intimately well-versed as my home department.)
This is important because the overlap in methods, mechanisms, and concepts is undoubtedly enormous. When we talk about migration, labor, local foods, even gentrification, the rural is an increasingly important site for understanding. And when we talk about 'regional studies' and about 'mega-regions', the rural is part of the equation as well (I attended an incredible colloquium on China's Urban Futures last week where rural issues were absolutely integral to understanding exploding megacities like Chongqing or planned growth in places like Langfang between Beijing and Tianjin; and hasn't this always been the case!). Indeed, to that end, what about suburban sociology?
Conceding that the answer is probably a blurry one anyway, as it really is with many social science disciplines and subdisciplines - the point is to ask whether there ARE meaningfully distinct literatures here, with distinct canonical texts, distinct traditions, departments, and methods, distinct problems, arguments, and debates? Is this changing in one direction or another?