what are some rational criteria for deciding between those two responses to an unfavorable situation

Change has inside-out structure. You have greatest influence on yourself, so among the things likely to rank high in "can be changed with courage" are all elements of your personality, starting with your own thinking. Next comes your behaviour. A distant third is your body.

Other people are harder to change, the harder with the various distances that separate them from you: physical, informational, cultural.

Structures involving many people are correspondingly hard to change, but conversely can be leveraged to have influence on many others through a single effort.

Things beyond the thin organic shell surrounding planet Earth are in all likelihood beyond your power to change.