Adiabtic vs. Isothermal

Which process produces more work out adiabatic and isothermal?
I've looked around the internet but different sites say which one is better and doesn't explain why.
Does it make a difference if the pressure is released into the atmosphere?

This is mainly related to a question I have in a paper that asks whether or not a rocket would reach a higher height if had undergone an adiabatic process rather than isothermal.

Is the line steeper for adiabatic? How can you show this mathematically?

Thanks