As someone who did the move a year ago:

Rent is comparable, but the apartments would be very different. 1BD 10 min walk away from work in SLU can be found for $1500/mo with in-unit washer dryer, secured package room, etc. To get the same level of amenity would require going further out into the boroughs and being subject to the whims of the MTA.

Goods and eating out are more expensive, but that's because Seattle has its min wage at 16/hr already, and unlike New York businesses do actually pay their workers the minimum wage. (Paying under the table is rampant at minority-owned businesses; those cheap supermarkets in NY Chinatown didn't get there through mystic eastern business practices.)