Visa status

I have been offered a fellowship , which is accredited and very much the kind of the program I was looking for, but they offer onlyJ1. Simultaneously I have been following up with another non accredited program from the premier league med schools where they offer H1B , but the interview process is still going on . The premier league program doesn’t offer any futuristic roles in the institution but the fact that I will have a H1 B and the profile of being trained there will have huge impact , if offered. How do I clear the dilemma.