Difference between あらそう and あらがう Both seem to mean contest, resists. Is more about verbal protest? And related to action such as rebellion? Is there an overlap?

There is a slight difference.

is to fight with, to compete for something, <

is to oppose, to resist, to go against something <

Simply put, you can for 1st place, but not . On the other hand, as a soldier, you can a direct order from your superior if you find it immoral, but its's not something you can .

Either word can be carried out verbally or via action, so that wouldn't be the defining difference.