I sort of go with both at the same time, I let the mechanics drive the flavor and flavor drive the mechanics. I usually come up with a concept first, then figure out the mechanics for it, and then further develop the flavor based on mechanics.

For example, my 5e pugilist character that focused on grappling and had a snake theme to her (snake tattoos and moves inspired by snakes like constrictors) was developed in PF2e as an Animal Instinct Barbarian (Snake) with Wrestler archetype for exactly the same flavor but more mechanics better suited for what I was looking for. I didn’t want to go monk since the only snake-themed monk stance is more focused on Poison (Cobra Stance) which isn’t what I wanted, plus she’s more of a rough brawler type than mystical monk type.

I usually start with a very broad flavour concept, then figure out how to do it in mechanics, and use that to flesh out the details of the flavour.

There have been times when I’ve come up with a very detailed flavour first and then gone for mechanics later.

The only time I start with mechanics is with one-shots or other times I don’t particularly care about the character themselves.