Prestige - Associate at Mid-Tier BB vs. MM PE (<$1bn Fund Size)

What is the relative prestige (as assessed by people outside high finance) of being an Associate at a mid-tier group at a BB bank vs. an Associate at a MM/LMM Private Equity shop. The only looks my group typically gets is from smaller shops (sub $1bn fund size) that focus on small deals.

Currently an analyst, wondering whether it's worth staying for the promote or exiting.

I understand prestige isn't everything (obviously) but my long-term goal is outside finance, where the name recognition would factor in.