Research Assistant Professor vs Post-doc Recently, I have completed my PhD in Biomedical Engineering from a 25 - 30th ranked USA university and got  a Post-doc offer from a 9-12th ranked USA University.  To keep me, my PhD advisor offered me a non-tenured tracked Research assistant professor (RSP) position with 1.5 times of offered Post-doc salary. I will be funded through my advisor grant and need to conduct research related to the funded project. However, I will also have the independence to pursue my research interest and apply for external funding. I have a very good relationship with my PhD advisor and good publications in my PhD. Eventually, I want to get a tenure-tracked faculty position. What is best for me “stay in my current university as an RSP ” or “ get the post-doc position in the more reputed university”?
I think you need to think about what that post-doc position can really offer you. Going from a 25th-30th University to a 9th-12th University isn't that significant, since the precision of ranking schools is iffy, at best. Therefore, think about what opportunities the post-doc will offer you: exciting research? Connections/contacts? Does the PI have a solid track record of post-docs getting tenure-track positions? On the other hand, being a non-tenure track research professor may be the better option if you think you can get enough data to apply for a grant. The bump in income is nice, too, especially given the high cost of education in the USA. I'm guessing you probably don't have student loans from grad school, but what about undergrad?

tl;dr- Post-doc:may lead to tenure-track job, possibly better contacts? Research asst prof: may lead to tenure-track job, but with better interim salary.