Both routes are great but there are a few differences that may tip the scale for you. As far as the passes go, the climb up out of Skagway is steeper curvier and shorter to get up to and over. The Haines pass is a lot more gradual. There's still curves to it but they're a lot more gently sweeping.
Another big differences is availability of services and options. Out of Skagway, you'll go through Fraser and Carcross and if you choose Tagish, before getting up to the Alcan. For the alternative route, you'll have services at Mile 33 Haines highway and then nothing until Haines Junction. That's about three hours to get there. A bit less on time getting into Whitehorse from Skagway.
Time wise is probably close to a wash. Its a couple of hours from Skagway to Whitehorse but then you've got to make up the hour and a half or so further to the Junction. Haines to the Junction is about three hours.
I prefer the Haines highway. You get above tree line after the border and get lots of nice wide open scenery that lasts for long stretches. There's less traffic as well and what there is can be passed with ease (RV's or Canadians towing crap). The other way is nice too though with some amazing views but just a bit more traffic from being a little more accessible from Whitehorse. The stretch between Whitehorse and the Junction isn't that interesting and things get a little busy through Whitehorse as well but if you're jonesing for a Tim Horton's or a stop at Canadian Tyre, Skagway it is. Either jumping off point is a gorgeous boat ride.
My other bike is a kayak.