I'm not sure about "cheaper"...dollar to dollar, it may be, but it you earn in Canadian $$ and have to pay for your training in US $, not to mention relocate, I don't think it would be cheaper. If you say have family somewhere that could help you out with living costs, say, it would be different.
As far as the immigration issue, unless you already have the right to live/work in the US, it really is incredibly hard to get into the US job market. Not trying to be negative, but it was something I looked at for years and never saw a way to break into. Not saying it's impossible but it takes a long, long time - sometimes even IF you marry a US citizen!