Why does damaging something sometimes make it more powerful?
Well in both cases you cited it relates to released energy that was somehow blocked because of the danger of its release. 
In Dragon Ball, I remember the scene near the end of the fight with Frieza where Goku tells Gohan something like this: "If the forces inside of me start unleashing, it will destroy this planet. You have to get out".

In Evangelion, we learn that the armor of the Evas are actually blockers to prevent them from going berserk, also hiding the true nature of the Evas, that they are composed more as a human would be, with skin, flesh and organs, than as a robot.



So these two things are common: the released energy that comes from hard, critical situations, near death experiences, and the revealing of the true nature of something, the dark forces inside all of us. I think it could be symbolic of the awakening of the unconscious part of the self.