I have been on F1 visa as a student for almost 5 years and will start my postdoc job soon. I wonder if I should apply for OPT or H1B visa for the postdoc position for better tax benefits?

If you have spent 5 years on F1, then you are not exempt from residency. On both the OPT income or the H1-B income you must pay SS tax, Medicare tax and income taxes.