Weapons Free uses both. You roll base values and then tell a story to earn points to increase these scores. I selected this mechanism because it includes some randomness from the initial die rolls which I find good when it comes to taking players out of their comfort zone.
In my opinion playing with low stat characters is a lot of and I've found it motivates a lot of roleplay. So to maintain this even with high stat characters I've attached a story line behind each extra point players add to the rolled values. This is done by what is know in game as saints and daemons. Background stories that explain why the character has those bonuses, but also come with emotional baggage. Which will undoubtedly become useful later on in the adventure, buahahahahahaha!
Still some players expressed their concern for the initial die roll and wanted all randomness taken out. Although it isn't something I'd endorse, it can be easily solved by adding a minor change to the initial attribute mechanism in the game. As a player you can go down the random road or chose something more static. Either way you'll end up with some value you'll have to then improve with saints and daemons. That way you end up with a story for your character which I find to be a key element for the game.
Thoughts? How do you prefer to roll your stats and how are they related to your character's background?