Weak to strong implies that the MC has strong motivations, perhaps revenge or the desire to protect someone, pushing him to become better. This desire pushes him to train and encounter new people and places. It provides many great opportunities for developing the MC as a character. If he starts off childish, you can show him mature and become much more level-headed. If he starts off vengeful, you can show him questioning the morality of his course of action. All this can be supported by side characters and subplots.
An overpowered protagonist has no reason to engage in any of these activities. He has already reached his pinnacle and presumably the goal that drove him to become powerful. Developing his character more becomes harder, but not impossible. You can show him go from a hard man who doesn't care for beings he perceives as lesser to seeing them as worthy of respect, regardless of their lack of power.
Each character type can be good when done right, but I prefer weak to strong.