what happens when a character has both?

Do you mean some other talents? I'm not really seeing possible the conflict.

Balance lets you recover strain based on Force Points rolled at the end of an Encounter. Invigorate adds Success and Threat based on Force Points to an Ally's Agility/Brawn-based skill check.

The AoR Beta version of Invigorate was a poor man's Balance, but got changed during that book's Beta Updates to do something quite different.