We are more restrictive in that respect, yes.
I know little about Canadian law. I know there is, or maybe was by now, a long gun registration requirement that ended up costing a LOT of money for little return. I thought I heard that it had be done away with but I really don't know.
I also know that, other the last several years, changes in firearm and hunting laws in Canada has caused a rather large drop in the numbers of Americans that travel up there to hunt. Which has led to a lot of small business going out of business.
I know several Canadians, that hunt in Michigan, that have moved all of their long guns to friends they had in Michigan to avoid that registration. I don't know much beyond that.