Now if you had to step through the double hatches of a weather porch of an Antarctic base into the freezing weather outside with nothing to wear I think the answer would be obvious. Nothing to wear means stark bollocky! nude! naked! Better to be dressed up with no place to go and stay inside.
However, I doubt that was what the questioner meant. Even so, would it be better to be dressed up with no place to go and to feel embarrassed and misery and yet perhaps meet people who could change your life for the better just by your meeting them?... In Australia we have a saying, "You never know your luck in a big city."
If they were wearing tuxedos and fine ball room gowns and you only had your blue jeans, slip slops and a tea shirt you might look out of place, but any real mental suffering would be on your part, not theirs. And at least they would remember you. You wouldn't be a non-entity.