The cost of living difference is very significant. I am an American living in Canada. I have never lived in Vancouver but I have lived in Phoenix. I can say that Vancouver will be MUCH more expensive than Phoenix.
The greater Vancouver area has a population of approximately 2 million people. The best city to compare Vancouver to would probably be Seattle although the Seattle MSA is much larger with 3.3 million people.
In general, everything in Canada costs quite a bit more than in the US. In my experience, this applies to groceries, clothing, other consumer goods, car insurance, fuel, and just about anything else you can think of. Here are some examples...
Sales taxes - 45% higher in BC
Phoenix - 8.3% (state, county, and city combined)
British Columbia - 12% (GST and PST combined)
Gasoline - 35% higher in BC
Phoenix - $3.88/gal
Vancouver - $5.23/gal
Housing (purchase) - 414% higher in BC
Phoenix (Maricopa County) - $222,450 average house price
Greater Vancouver - $921,000 average house price
Phoenix House and Condo Prices - Phoenix Real Estate Prices - March 2008
Average house price in Greater Vancouver nearing $1-million mark
I have found income taxes to be more here in Canada as well. If your employer in the US currently pays all or most of your health insurance, you will personally pay out more through taxes in Canada. On the other hand, if you have been paying all of your own health insurance premiums in the US (very rare), you might actually save money on health related expenses.
The cost of living picture looks pretty bleak on the surface. However, if you can make significantly more money in Canada and, more importantly, will enjoy life more here, I wouldn't let it stop me. I personally like living in Calgary and have no regrets about moving here. Although, this may have been different if I lived in any other province. Alberta has the lowest tax rates in all of Canada. There are things I dislike, like the medical system, high tax rates, and high cost of goods but those do not outweigh the job I love and the great friends I have made here.
Good luck