Who has a cheaper tax ny or nj and if I live in nj and work at home every day but one day which I work in NY and all my taxes were withheld in NY what's my best option 1- to file as if I work in ny every day 2- to file that I work in nj every day or 3- to prorate the days and take a credit from ny to nj

I already answered this question.

NY has the HIGHER tax rates.

You must file BOTH NY and NJ. You file as a non-resident in NY and pro-rate your wages between when yum worked in each state. A memo from your employer (to be included with both tax returns) will help justify filing this way.