first of all, congrats for the startup offer.
I would personally make these considerations:
Is it your 1st work experience?
- In this case, if you are very young (fresh from uni), consider the importance of having a strong brand (if you don't have any) on your resume. That will help you in the future. This could be either a good startup (VC-backed or PE-backed) or a company like Accenture.
Is this your first full time job?
- Spend time on finding the right fit and understand if you are interested to start right away in an entrepreneurial environment vs a consulting environment. They tend to be quite different settings.
To answer your question about rejecting the startup offer
It is a matter of professionalism. But considering the fact that startups need very passionate people, better to leave the startup rather than staying there, but not being committed anymore because you are more interested about working in consulting.