Just ran a mission with Bonewidow since its exalted blade wasn't leveled up. Got the victory screen and both archweapons appeared. Both leveled up to max rank. But when I went to my armoury, the Phaedra was level 19 again. The Ironbride kept the exp it earned.
I brought the Phaedra (equipped on my Voidrig Necramech) onto two missions in the Orphix Venom event. It was level 19. It levelled up to rank 30 inside each mission. At the victory screen it stated they were max rank. When I went to my armoury, they were level 19 again. Now on the victory screen, the Voidrig's exalted guns did not appear (I did use them) and mine are at max rank. I believe the exp system is confusing the two Archguns up, preventing my Phaedra from being levelled up.