I just returned from a Great Parks tour from Wyoming through the Icefields Parkway and on to Prince George. From our perspective, the winds were blowing hard in our faces or at our sides and the hills were both long and steep.
People we met along the way seemed to think the hills were long and steep, but that they had a lot more tailwinds.
As snow kept the Going to the Sun Road closed until July 2 this year, bikers going both directions had to bypass the park.
I think you might make your decision based on logistics. Shipping a bike to Canada can be very pricy, and your bike could be held up in customs, as my friend's cycle was. (She also had to pay 5% duty and taxes on the value of the bike before it was released. She estimates it cost her over $500 to get her bike from Denver to Banff. And she had been given no warning about this by Fed Ex or the bike shop to whom she shipped the bike.) We carried the bikes as luggage on our flights home for $50 each.
It's my belief that headwinds, hills, and long days in the saddle make us stronger and promote great memories. So maybe the direction doesn't really matter at all. The amazing scenery and people along the way make up for the hardships.