probably depends on your citizenship. It seems from your question that you are neither a Canadian nor an American citizen.
Even if you are a landed immigrant in Canada, you will still need
a H1B (or J1) for your residency.
My own opinion, for what that's worth, once you hold a Canadian landed immigration status, US may look upon your visa application more favorably.
Do you have a H1B already? If so, what are the rules on the portability of the H1B visa? I dont know.