Given the primacy of our Constitution and the Supreme Court's role in interpreting whether a law is consistent with our our Constitution, choosing justices is a rather existential question.
And that's the crucial difference: if a Supreme Court judge in Canada starts misbehaving I guess Prime Minister can dismiss them just as easily. In the US judges are appointed for life, so if the wrong person gets appointed that choice will haunt us for a few decades.
The result of this is basically higher quality legislation: no loopholes to gain this Senator's support, no watering down or poison pills; but also, no extremist bills with clauses to trade away to buy support. The gov't passes the legislation it wants to, in the form it wants to, for good or ill. As a result, I believe, matters reaching the Supreme Court of Canada really are more narrow legal issues, not another avenue of attack on legislation. There can be significant rulings with broad implications, but overall, Canada's Supreme Court isn't a battleground because legislation isn't a mess offering a variety of vectors of attack. It's more internally coherent.