$20K less each year is $80k less over the four years. That $80k you would be saving could help towards your medical school degree. Add all that into the fact that you’re in-state for UW-Seattle, one of the finer public universities in the country. I also don’t at all consider NYU to be a better school, but that’s just me.
Save the money and go to UW-Seattle. You’ll get a very fine education there.