Start at BB or boutique as VP

I’m new to IB and making the pivot later in my career. Interviewing at BB and boutique at VP level. Is it better to begin a new career in IB at mid level at a bulge or a boutique and why?

My goal is to make it to MD as quickly as possible.

My instinct is to start at BB then move to boutique after obtaining MD level because I understand boutiques pay more. However if I start at a boutique, which would likely come with higher $, I worry the lack of bigger name recognition for future career opportunities down the road.