I can get YMIR mechs down to the same amount of health with the grenade launcher and still have ammo to spare.
Note that it takes 20 grenades to do the same damage against health as 1 Cain shot, or 16 grenades against protection. For every 100% of Cain, you only get 10 grenades.
So no, Cain is more ammo-effecient than grenade launcher, or any other heavy weapon for that matter. The discrepancy between your experiences and the actual damage values is most probably due to the fact that your team is helping you do the damage, and not because the grenade launcher is more effecient.
Also don't forget that with the Cain, you're only out of cover for 4 seconds, and even then you can shave that to 2 or even 1 second by charging the weapon up behind cover and exposing yourself only when the shot is about to go.