Marko,
I’m hardly an expert (my last experience with INS was more than 15 years ago, when my wife got her US citizenship). But a few observations:
There’s a difference between temporary work-related visas for high-skill workers (H1B) and permanent resident visas (the so-called “green card”).
Last time I looked, permanent resident visas were based, in part, on country of origin - good for you (Irish get a double quota, thanks to Ted Kennedy), bad for your girlfriend (poor/populous countries like Malasia are generally a long wait). The base assumption is a green card is a stepping stone to getting US citizenship (not always true, but the base assumption) and carries the automatic right to work.
I’m not up on the details (my company hires H1B holders, but I’m an engineer, not an immigration lawyer), but H1B visas are based on needed skills, not origin. However, they need to be arranged by the employer/agency, and if you lose your job (or want to change it) you have to go through the paperwork again. If you’re between jobs, you have a limited time (30 days?) to find a new employer and start the process over again.
Since you’re both high-skill workers, you have a better chance at getting a H1B than most (though as Redwolf can testify, IT jobs, even in Silicon Valley, are harder to find than they were during the boom years). But if you’re planning a short “working holiday” kind of visit, for a few years at most, it may be the easier route.
If you are thinking of moving permanently (BTW - even if you get US citizenship you are no longer forced to give up your “other” citizenship) you might be better off going the green card route - you can try to switch from H1B to permanent once you’re here, but it may be easier to do this from the start outside the US. (This is where an immigration lawyer would really help).
A note - if you are really a couple, and plan to stay together, you’d probably be better off if you marry, because the US immigration department gives no special consideration to non-married couples. There ARE “fiance’ visas” for fiance’s of US citizens & permanent residents, but they are reputedly hard to get. Again, see your immigration lawyer.
Don’t know what the situation is in Canada, though I’ve heard that it’s easier to get “Landed Immigrant” (I believe that’s the equivalent of the US “permanent resident”) status than in the US if you’ve a good education, money in the bank, etc.