Conservatives, though I suspect much of the reason they're more moderate than the Republicans is because of how much more liberal the Canadian society and government structure is than the American one is. If the Conservative party existed in the United States, I think there'd be less incentive for them to be so (relatively) moderate.
I agree, but isn't that true for all political parties in democracies? If you want to stand any chance of winning elections, you have to be relatively close to the center of the country's political culture.
The current Republican party will also "moderate" somewhat as certain politically disputed things become "normal". For example, I doubt most Republicans will be disputing global warming in a few years, simply because it's turning in to a widely accepted truth.
The same way that certain programs that were enacted as a part of the New Deal aren't seriously disputed by any mainstream politicans.