Its Canada it rans and snows everywhere. Some places get more snow some get more rain. Lots of people happily live in both provinces and some are not happy. Try thinking in terms of affordability.
Alberta has no PST only GST at 5%
BC has the HST soon to be the PST again rate is 12% at the moment.
Cost of buying a home in both provinces will vary big cities or suburbs or rural area.
Transportation costs drive everyday or take public transport.
Groceries are about the same price in each province regardless of the tax rate and will also vary between cities, suburbs or in the middle of nowhere.
Climate in Alberta is probably colder overall i.e. longer winters.
BC has one hockey team Alberta has 2
BC has more Starbucks whereas Alberta has more Timmies
Alberta shares the border with Montana BC shares it with Montana, Idaho and Washington State.
BC has a bigger international airport
BC has a MSL team for football Alberta doesnt.
You can ski, fish, cycle and a shit load of other things in both
You can find fish and chips, expensive cheese, ribena and a host of other UK goodies in both.
Ive spent time in both but choose not to live in either.
Both have lots of bad drivers.
BC bud has a higher THC content than Alberta bud.
BC has Kokanee Alberta has Big Rock beers I drink neither.
Im bored hence passing time to help you decide on BC or Alberta.

BC has TGI Friday's.