Does BB name brand actually provide a lot of value?

Recently got in a civil debate with a friend at a BB (GS, MS) who felt I wouldn’t suffer much, if at all, from being at an EB (EVR, CVP) if I wanted to leave the industry into something more niche (my interest). Ultimately, his argument boiled down to networking with people and knowing your stuff will get you to your destination irrespective of name brand bank. But all things equal, I’d assume the BB gets the slight edge. Would appreciate some input here from more experienced folks.

P.S. I know on this platform we tend to praise the “name brand” a lot, so this post may seem redundant, but essentially asking for real world, tangible examples here — to the extent possible.