Cleaning walls or painting
The answer is "clean walls AND paint," if you're going to paint at all. Even if you do decide to paint over a stain you can't remove, you still need to clean the wall to make sure the paint adheres properly.

I use TSP to wipe down the walls or surfaces prior to repainting. It cuts the level of surface gloss, really cuts through grease, and gives you a nice clean surface for new paint - all with a quick wipe down and minimal scrubbing.