What is the difference between an Arcane Focus and a Component Pouch?

Reading through the Player’s Handbook, I’ve noticed that the Sorceror, Warlock and Wizard classes can all take either an arcane focus or a component pouch. My understanding is that an arcane focus takes the place of the component pouch for most material requirements, so having the choice seems meaningless.

What are the differences between the two, and in what situations would each be better than the other?