Offer 1: Big PE fund (30bil AUM) 3 months intern, with high chance transferable to Perm Analyst after internship

Offer 2: Small PE fund (1bil AUM) Perm Analyst 

Salary: Similar for perm roles 

Job Duty: Similar 

Background: Final Year, Nearly Graduate. Struggling between a better but less stable internship or worse but stable perm role. 

-Is the brand name / starting company in PE important? 

-Anything I can do? 

Thanks a lot!🙏🙏🙏