Lots of discussion about the boundaries. Political boundaries and other. Locals don’t seem to care one way or another. But here the reality. The border between Canada and the U.S. runs down the middle of the Niagara River (sort of), but the river twists and turns and the border moves slightly to stay in the middle. Following me?
Now it gets to the Horseshoe Falls (or Canadian Falls as some prefer) area and the border takes into account the two fairly large turns and width of the river above the Falls. So at the Horseshoe Falls, the border runs through (the edge of) Terrapin Point which is part of Goat Island, which is in the U.S.
Thus everything on the west side of the border line is in Canada, while everything on the east side of the border line is in the U.S. Sooo, that means that the Horseshoe Falls, or Canadian Falls (whichever you prefer) is entirely in Canada save for maybe a foot or so on the easterly edge of the Canadian Falls.
The American Falls and the Bridal Veil Falls are both in the U.S. Thus if bragging rights are at play here, then Canadians probably tell people that the Canadian Falls are entirely within Canada, and they would be correct.