NJ taxes are much higher than NY. Also depend on the town it may be very different. On the same token, houses are usually lower in the price(again, depend what town). You should consider school, transportation, crime rate, proximity to every day needs: grocery stores, shopping, schools and transportation. That's were NY is stand out. I specialize in Staten Island ,NY . We located right between NYC and NJ and we are probably the choice for you to consider.
So...........You would really have to list some specific towns, and a price range, and then you could compare and contrast what the taxes are, both, in NJ & NY.
For example, a townhome in harding, NJ or E. Hanover, NJ can have taxes in the $4000 (or less) range, and sell in the 400,000+ range.
A similarly sized/priced unit in another town (for example - W Orange) can have taxes of $12,000 or more.
Your best bet is to reach out to local agents - give your price range, housing requirements, and, ask what the taxes will be............you will then see what you will be able to buy in that range.