You can move to the US on the TN visa (as long as NAFTA is still valid). I've met programmers from Canada and Mexico who are on the TN visa.
The only benefit of an H-1B over TN is that it is a dual-intent visa, and you are guaranteed to not have "immigrant intent"-related trouble at the border. However, there was a guideline issued by the CBP back in 2008 that stated that a pending employment-based green card application (I-140) would not alone be considered as immigrant intent: https://www.hooyou.com/news/news021709tn.html Quoted:
"A recently published authoritative letter from the U.S. Customs and Border Protection Agency (CBP) addressing the TN nonimmigrant visa category offers new and definite insight on the CBP’s policy for determining immigrant intent. In the letter, dated April 2008, the Executive Director of Admissibility and Passenger Protection Programs details clearly that filing an immigrant petition (I-140) alone is not automatically considered a demonstration of immigrant intent, and aliens with pending I-140s may still be admitted into US with a TN visa."
I don't know if that policy is still in effect, but if it is, then you have nothing to fear, and your employer can apply for your green card. The programmer from Mexico on TN that I knew actually had USCIS approval of his TN status. For TN status, USCIS approval isn't necessary, but it helps avoid problems at the border even further: https://www.tnvisabulletin.com/nafta-tn-blog/2012/4/12/cbp-m...
Why would it affect you?
So again, how do H1-B changes affect a Canadian?
Source: I'm a two-time Canadian > US TN-to-H1B and eventually bailed out of the process by marrying an American.
An H-1B gives you a defined 6 year window with doctrine of dual intent allowing you to pursue a green card, which a TN status does not.
All this on top of worrying about work, relationships, personal health, and always trying to catch up and learn the "fundamental" bits of knowledge required to do my job. Sometimes I feel like I wasn't born with as many cores as others :(