Again, it depends on what look you want. Pushing usually doen't really increase the ASA of the film, but just compensates under exposed midtones and highlights. Usually you lose shadow detail too. If you want a grainy look with black empty shadows, pushing can give you that look.
If you pull, you'll get better shadow detail, but you can pull too far and your negs might give grayish prints.
These aren't necessarily bad things, but you can use it in your repertoire of looks. It's a creative tool.