Great Place! Lucky girl.
We had a recreational property there for 15 years so drove both routes often including in winter. We were not towing.
My observations. The Crowsnest is slightly longer but not enough to be significant.
The Parks route is probably a little hillier but any major ones have passing lanes. Sometimes the snow encroaches on the outer lanes reducing the effectiveness of the passing lanes. The worst section is often the 5-6 km from the Trans Canada up to Storm Mountain. The snow tends to pack on there probably because it is a north facing hill.
I don't think the differences in the routes are significant enough to make the decision. I believe it is a weather, road condition decision.
If the weather is at all inclement I felt more comfortable with the Parks route as it avoids the heavy snow belt around Fernie and the wind in the Crowsnest. I think this sentiment was shared by quite a few locals. We only took the Crowsnest because of family connections.