Pump out or emit are both fine. As you probably know, if you have a choice of a phrasal verb (pump out) or a word from a Latin root (emit), the phrasal verb will be the more informal option. 'Emissions' is more a more formal word than 'fumes' in this context.

I'm not sure if I have ever used pump out in this situation. Here are some examples of what I might say. A hybrid car emits less exhaust than a diesel truck. Because there are more cars in big cities, emissions levels are higher. This car is emitting a lot of exhaust fumes.