The party first fights them at Dollet where Biggs is attempting to repair the damaged radio tower there. Although he succeeds and battles the party with Wedge's help, the tower's activation disturbs the Elvoret who blows them off the tower with its Storm Breath.
Apparently demoted, the two later appear at the D-District Prison as guards. When one of the security guards has them deal with the party for causing trouble, both the party and Biggs and Wedge are horrified, but the two use the chance for revenge and battle the party. They are again defeated.
The two appear one final time inside Lunatic Pandora near the end of the game. Apparently now demoted even further, they contemplate the futility of their service to the Galbadian army and decide to quit and walk out without even noticing the party.
Biggs and Wedge are little stronger than other Galbadian Soldiers in battle, estentially possessing the same attacks, but with slightly higher power and they have more HP. They are quite easy to beat.