I didn't actually mean that it depends on the "game system", but on the game at hand. Sometimes I go in with a solid concept, other times I love to let the dice guide me.
One of the tricks I had MASTERED for CyberPunk 2020 was the creation of a solid and cohesive character background built up within 15 minutes of rolling the character background on the lifepath tables - without changing any of the results rolled on said tables.