I hesitate to respond, because I really don't want to argue Cool Arrow. But in NM residents get a minimum of 78% of the tags this year. Starting next year it will go to 82% from what I have read. That's a pretty big advantage over the NR.
Of course, there are more residents applying for the available tags than non-residents, but in reading the draw odds reports put out by Game & Fish the chances of a resident drawing a tag are still better than a non-resident.
No doubt some units are tougher to draw than others. I have never drawn one of the high demand units like the Gila, etc. The second tier units don't receive as much attention.