These two series both have heavy dosages of mecha, though its mecha done right, when there ARE casualties and sacrifices are made, though Gurren Lagann is less thinking, it still has the right combination of elements to keep you glued to the screen and want more. Think Gurren Lagann as a lighter, less intelligent type, that has a wider scope then Code Geass.
Though the series main characters are vastly different and Gurren Lagann might be considered a "lighter" anime, both of these series engaged me and made me addictively watch as much as 20 eps a day. Additionally, both series fighting is done in mecha and they fight against superpowers with little more than their wills.
Code Geass and Tegen Toppa Gurren Lagann both involve mecha, and of course, lot's of action. Although the fighting in Code Geass is essentially against one enemy, and in Gurren Lagann, the enemy/opponent varies, it is still clear that there is a protagonist and antagonist in each story. Both take place in the future, as well. In both, the protagonists is a strong character, who has the support of several characters. Both are exciting, and involve a lot of action, as well as some comedy and romance. =)
Both are mecha animes that envolve around war. Both implement stratigies in their battles however Gurren Lagan is a bit more silly and random. It's like you combined Code Geass with FLCL. But if you like Code Geass defently try out Gurren Lagann
Similarities : mecha, heroes starts as rebel force fighting against much more powerful opponent, there is one strongly determined leader to whom everybody look up to. Mysterious power working behind scene.
Differences: while Gurren Lagann is mainly using comedy to relieve tension after dramatic moments (and there is plenty of those), Code Geass use more serious note in its storytelling.
Mecha,masterminding about something that very badass,future world and super badass duel scenes among robots are main features that both anime shares.
Thematically, both series are very similar! Both include large-scale mecha fights, and a plot about overthrowing the government. Gurren Lagann is a great show and well worth a watch.
Both use a Mecha genre to house underlying intellectual questions and reflections on modern society and the human experience. Both of the anime follow the Hero's Journey very closely (look it up), and follow similar themes of sacrifice, morality and the human condition of betrayal. Both series have amazing character development, although Code Geass starts off a little slow compared to Gurren Lagann in this sense. I'd really recommend persisting past the first 3-4 episodes if you find them a little dry, you won't regret it.
Both shows are mechas, and ones that non-mecha fans would enjoy. In Code Geass you have a mysterious power as well as interesting tactics, Gurren Laggen has unlikely wins through awesome scenes. Check both out