Why must bacteria outrun diffusion?
Because then it wouldn't be going anywhere, and the first part of the sentence is specifically about traveling.

Without more context that might make me wrong, I think the statement is intentionally tautological and is just meant to set up a problem to solve. 

By "better or worse" I think the author means to generalize about conditions that an organism may prefer: nutrient concentrations, temperatures, etc. 

Restated, I think the author is roughly saying "For cells to spend more time where conditions are best for them, they have to move on their own power."