> I'm not sure where you live, but American conservatives favor power in the states
American conservatives say that in the context of debates over federal engagement in certain types of government programs as a reason for opposing them there (which, incidentally, the same conservatives also oppose at the State level), but not about the kind of programs they support, like, say, national defense.
The areas that American conservatives make the biggest stinks about state power are identical to the ones where they make the biggest stink about the function not being a proper role of government at all.
> American liberals favor power in the federal government (i.e. centralization).
Er, no, American liberals don't. American liberals are often characterized as supporting centralization by American conservatives when they support the federal government doing things that American conservatives don't think government should do at all. (They are, surprisingly enough, not accused by American conservatives of "opposing centralization" when they oppose the federal government doing things American conservatives think it should do, e.g., spending more money than the rest of the world combined on national defense.)
Both American conservatives and American liberals tend to conduct multipronged efforts to get the same general policy preferences adopted at both state and federal levels (and tend to push all levers of power available, executive, legislative, and judicial -- and, at the state level, direct citizen initiative) at both levels.
In addition, American conservatives tend to accuse American liberals of centralization whenever they push a policy conservatives don't approve of at the federal level (particularly through legislative action), of seeking to "overturn the will of the people" whenever they seek to overturn a policy conservatives approve of through judicial action, of dictatorship whenever they seek to implement policy conservatives oppose executive action, and of infringing on the authority of the executive when they seek to implement a policy conservatives disapprove of through legislative action, at least, when the executive is in hands viewed as friendlier to conservatives.