Gurren-Lagann is a show with very meaningful substantial content, with a very strong opinion behind. The entire work was based over the delivery of this content.: The narrative style is amazingly well-written. The director may take plot as medium rather than as objective, but thanks to the skill behind the script the series manages to make the usually superficial storyline part of the theme itself.
Symbolism, theme and ideas are not only the heart; they're one with the entire work. Not hidden underneath but neither simplistic nor tacked in. The nature of human progress is the core theme. Progress as in moving forward, both the consequences and achievements from such an action. From episode one it was always about "overcoming" the past- the legacy of your ancestors. Kamina's desire was to go beyond those limits determined by the elderly, a glorification of young defiance. The brilliant ambiguity comes when taking into account Kamina's inspiration was no-one other than his father, an ancestor. The DNA symbolism is fulfilled by the storyline itself: the instance of going against your roots while embracing them mimics the double helix.
Code Geass was just a badly planned mess with empty thematic content.