Specifically, Evangelion is the biggest contrast to Mazinger Z. Getter Robo and Mobile Suit Gundam, and many other mecha anime run the gamut, but Mazinger Z is important because as the genre's progenitor it plays each and every one of the genre's conventions completely straight.
Consider the protagonists. Kouji Kabuto is a hot-blooded, young, idiot hero. His victories are the culmination of his fighting spirit and the Mazinger's power. The Mazinger is a gift to him from his grandfather, who'd spent his life building it in preparation for conflict with the Mecha Beasts. Shinji Ikari, meanwhile, is a troubled young man who is both a coward and prone to over-thinking things. His victories are less a result of his indomitable will and more often the result of something within him breaking. His father had spent his life building the Evas to combat the Angels. Herein we see that Evangelion dedicates itself to setting itself up as being your standard super robot show while simultaneously preparing for its deconstruction. The Mazinger Z is supposed to grant Kouji the power to be either a God or a Devil, a power which Evangelion Unit 01 also is said to hold.
Over the course of the series, Shinji attempts to undergo more or less the same path that all hot-blooded mecha heroes do. He rises, only to fall so that he may burst from the ashes and prove his true worth. For much of the series, though, Shinji fails again and again at doing that. When Shinji attempts to be a hero and save Toji and confront his father using Unit 01, for instance, Gendo quickly gains the upper hand both times. When Kaworu presents Shinji with an unwinnable conflict, rather than doing the impossible and finding a win-win situation, Shinji gives in to one of the two choices. What's most interesting of all, however, is that where much of the series is spent showing how the standard conventions of a giant robot anime would have terrible consequences or be moments of unfathomable horror, the show's ending is almost complete turn about. Shinji's realization that he can change, that he can find love and that he can overcome pain is his doing the impossible and finding a way out of the set parameters.