Uchuu Kyoudai, Shouwa Genroku Rakugo Shinjuu Recommendations
They're (like) brothers, have very different personalities, and are together in the search for a dream. And "together" does not mean it won't be conflict, angst and envy between them.
Both series will make you learn a lot: In Rakugo Shinjuu, you learn a lot about the rakugo art and japanese history and culture; in Uchuu Kyoudai, you learn about astronautics and space.
The drama is very well presented, even the side character's stories manage to captivate you. You'll end up crying, laughing and struggling together with the characters - they're crafted like real people.