Very strange recommendation, but there's an arc in both where a character, who had previously been under a veil of mystery, had to approach their past and put things behind them, with both of these arcs including fighting an old friend over a woman. This recommendation isn't for the shows as a whole, but how these arcs parallel. They're both incredibly well-written and emotion evoking.
I assume more people have seen Bebop, so check out the Initial D franchise if you have the time.
Both involve cars: Tuning them, racing with them, and the like. While Initial D is more about becoming the best racer, Track City is more about saving the world. Oh! Track City's cars are remote-controlled, but that shouldn't matter.