Sue, wouldn't that depend on where you were going or coming from on your trip. If you figure you are crossing at the Coutts/Sweetgrass station, north of Great Falls Montana, I would guess the Alaska Hwy route would be shorter.
Now for you to go to Vancouver, I am sure your figures are correct in that the Cassiar is shorter, The farther east you cross into Canada or the US, the Alaska Hwy route should be closer. I often cross at Coutts, the go north for a ways and cut west to the Banff and Jasper and Yaho NPs, then cut up to Dawson City and take the Alaska Hwy on up. Other trips I will head on west to Prince George and to Kitwanga Junction to head north on Hwy 37, the Cassiar, to intercept the Alaska Hwy north of Watson Lake, 13 miles or so.
Don't believe I have ever tried to figure out how many miles each route is in distance.