I second pretty much everything
qtipbrit92 said. Although personally i was bored to tears with Lain, it is generally a well acclaimed title and indeed touches upon the issues you want.
If you liked Evangelion, you should definitely have a look at
RahXephon. The two series share a good amount of similarities theme and plot wise, and touch upon a number of similar issues ... although you will find the cast of RahXephon much less annoying. I like Evangelion a good deal, but ended up prefering Rah in the end.
Two other mecha shows that might interest you are
Zegapain and
Soukyuu no Fafner: Dead Aggressor ... incidentally both are my two favorite mecha series, although for different reasons.
Fafner shares a level of similarities with Evangelion as well, and the most remarkable effort of the series was the atmosphere - it had a well crafted sense of impending doom and despair woven through it, and the new facts you learn when deeper in to the series only reinforce that. It took me a few episodes to get in to the series, but i ended up highly appreciating it. The one ep OVA (watch it after the series) is among the saddest things i have seen.
Zegapain is generally different in its mood and approach, but it is directly connected to themes like survival of humanity and other issues you might find to your liking. The mecha design might take some getting used to, but its worth it. It is a very solid story with likable cast. Just remember when starting: everything is not what it seems to be
