How is the answer not Canada? The Tories are one of the closest parties to the GOP, even if it is too extreme these days. (Fidesz isn’t a great comparison given the somewhat tepid economic interventionism) I don’t think I need to go over parallels between the Democrats and the Liberals. Canadian politics has also often been compared to United States politics. Western Canada especially seems to have an affinity for certain types of American-style culture wars (especially those around energy).
Western Canada is clearly more similar to the US than anywhere else, but the Eastern Tories often have more in common with the British "wets" than any American equivalent, and the Liberals are far more dominant than in American politics, and the Quebecois political scene is totally non-comparable (and Quebec is a big part of Canada: 23% of the population lives in Quebec.)
I actually have to dispute this. Ever since the 1980s realignments in both nations that broke Democratic/Liberal Party dominance, the liberals have not far been more dominant than the dems have.
Since 1980 the GOP has been in power for 24 years compared to the Dems with 20 so the GOP has been in power 54.5% of the time .
Since 1984 the Tories have been in power for around 19 years compared to the Liberals around 21 so The Tories have been in power 47.5% of the time.
So while the Liberals are slightly more more dominant than the Democrats, its not far more and I wouldnt say any of the major parties in either the US or Canada have been dominant since Reagan's win in 1980 or Mulroney's win in 1984.