Boutique vs Large Firm Straight Out of Undergrad

I'm in my second year at a UK target (Oxbridge/LSE), aiming for a career in investment management (long-only or L/S equity). I've applied to internships at all the majors, but am curious about boutiques.

1. For investment management specifically, does a boutique internship carry the same weight as one at a big name? How important is the brand name compared to the actual experience?
2. Post-grad, would you recommend starting at a boutique or a larger firm for someone aiming to eventually manage a portfolio or even start their own fund?

Thanks!