How do you know if you need to replace the oxygen sensors or the catalytic converter?

Fault codes thrown by the car's ecm. Neither of these components usually goes bad on its own, their failures are generally caused by something else like a dead cylinder allowing unburned fuel to pass through to the exhaust.

Before you spend the money on either, figure out what other fault codes your car is throwing. If you replace a cat and still have unburned fuel reaching the new one, it will be damaged and you'll need to buy another cat (they wont warranty a failure caused this way)