Sorry for late reply, but maybe this will help someone.
I have been in the Yukon for over a decade and lived in BC for 15 years or so. I have also lived in other parts of the North, the prairies and even back East so I have many points of comparison.
Culturally, Yukon and BC share lots of similarities. First Nations culture is very important and many Yukon First Nations share cultural practices and history with Alaska and BC First Nations.
Whitehorse in particular is a "lifestyle" place with a mountain town feel -- people do a lot of outdoor activities here. It is a paradise for both old school huntin' and fishin' and snowmobiling as well as skijoring, snowboarding, SUPs, ultramarathons, backpacking, etc. If it can be done on mountains, rivers, lakes, or trails, people do a lot of it here.
One of my favourite analogies is that Yellowknife, NWT is to Edmonton as Whitehorse, Yukon is to Vancouver. All of them are great places, but their priorities and vibes are different.
I have only travelled to either, but since nobody else has replied here's my 2 cents:
The general vibe I get in BC is there are always people around the approximate vicinity. Meanwhile in Yukon, you can go out to the literal middle of nowhere and nobody will find you for some time. If you wanted to never see another person again, it would be much easier in Yukon than BC.
