From both Minfilia's description of the battle of Silvertear Skies and the actual cinematic we see of it, I'd say Midgarsormr actually pretty solidly defeated the Agrius by destroying one of its main engines. He was only killed in turn because he was wrapped around the ship at the time, and couldn't uncoil before it crashed. When Gaius said they defeated Midgarsormr, he was pretty clearly trying to put a less-entirely-negative spin on what was a crushing defeat. It wasn't actually the Garlean weapons that killed Midgarsormr, it was the explosion of the ship as it struck the ground--after all, he roars just before the explosion goes off. Also, Midgarsormr isn't a primal.

Personally, my own reaction to Shiva's battle with the Gration was somewhat more disappointment that she didn't outright destroy it instead of temporarily disabling it, since I feel she could have. But then, as the battle with Ravana illustrated, Ysayle wasn't actually all that great of a fighter, and her own dialog prior to using her crystal suggested that she didn't have any intention/expectation of winning. By that point, she was just... deeply broken, and had come to die while making her death count for something. It's also possible that, considering her general inclinations, dying in the act of hindering the Gration would actually be preferable to having won and so having the deaths of so many people--Imperial soldiers or otherwise--on her conscience.