Sales and Trading vs Investment Management

I am a beginner to finance looking into various summer internships.

I have an interest in stock market investing in particular.

I would say the priority for my internship (as it would be for most) is to learn as much as possible whilst also hopefully getting a prestigous name on my resumé to make it easier to get my foot in the door for later jobs. Naturally I have been interested in sales and trading as well as asset management.

I have searched elsewhere but have little success finding the following:

How do investment management firms (State Street, Fidelity, Wellington, etc) match up against bulge brackets in sales and trading (MS, Goldman, BofA, Citi, etc) in terms of prestige - what would the better path be in the theoretical world of receiving an offer from everyone and everything I applied to lol.

Also I have seen a few roles such as prime brokerage lie inside of sales and trading - are these less desirable (e.g. they may be middle office roles?)

Essentially, how would you rank roles at each of these firms in terms of the best choice?