Cost of Living:
BC and Vancouver in particular is probably the most expensive place to live in Canada.
Not just in terms of housing costs but everything from gas to groceries.Sales taxes are also fairly high.
Alberta on the other hand has much more reasonably price ed real estate,no PST and gas is probably the cheapest in the whole country.
Nightlife/Shopping/Entertainment:
Vancouver probably has the edge here although any large city will have a decent amount of good restraunts/clubs.Edmonton is probably better for shopping though.
Crime:
Both cities have fairly safe suburbs that are good for raising families and both cities also probably have inner city neighborhoods you want to avoid.As for the city itself I wouldn't be caught dead in downtown Edmonton after dark again.Lets just leave it at that.I have been to downtown Vancouver after dark and it's not bad at all.Most nights it will still be busy far after 10 as long as you stay by the harbour and other touristy areas and also by the areas where there is alot of nightlife.
I have heard there is quite a drug issue in Van city after dark but I didn't see it.
Transportation:
Vancouver definatly has more traffic and congestion than Edmonton.I also noticed that in Vancouver there were alot more speeders and agressive drivers(tailgaters,people not using blinkers etc.),wheras in Edmonton everyone seems to stay within the speed limit and drive in a much safer manner.
When it comes to public transport however I would say that Vancouver is alot better.The Skytrain is excellent and provides good coverage of the city.Edmonton does have an LRT system but it never seems to be used as much and I hear coverage isn't too impressive.
Bus service is probably so so in either city.
Weather:This is one category in which I think Vancouver always gets overrated bigtime.Sure winters are mild but it's always grey and alot of the time its raining.Extremly depressing.I have lived in London,UK so I know what this is like beleive me.Also yes its mild but our bodies are used to it so it feels cold.If its 6 degrees for the first time in march in Edmonton its the greatest feeling in the world.You could walk around in a t shirt and not be cold.In Vancouver its just going to be another dreary breeezy grey depressing cold day.Even in the dead of winter I would take -10 sunny and dry as oppossed to +5 or 6,humid,windy and overcast.I live in Saskatoon,SK right now so again beleive me!
Summers are about the same in both cities but Edmonton will get alot more 25+ days than the BC coast.
All in all I would go to Edmonton because Vancouvers high cost of living doesn't justify its benefits and I hate Vancouvers winters.