No one is after the One-Piece in the straw hat crew, not even Luffy.
As it was explained many times, each member has a different motivation to go trough the Grand Line:
- Luffy wants to conquer the Grand Line to be the pirate king, because the pirate king has the most freedom in the world
- Nami wants to draw the map of the entire world
- Sanji wants to get to All blue (wich supposedly is close to One-Piece)
- Zoro wants to be the biggest swordsman in the world (aka.: He need to defeat Hawk)
- Chopper wants to find the cure every disease
- Robin wants to learn the void century's history
- Franky wants to be on the Sunny Go when Luffy becomes the pirate king, so he can complete his dream
- Brook wants to meet Laboon when they finally get back to the beginning of the grand line
This is why they seem to be better than most of the pirates as they don't want to get to the end of the Grand Line to get rich.
Law only wants to find the One-Piece to become the Pirate King and because that's mostly treasure.