Total Recommendations: 4
This has a similar feel to Demon City Shinjuku but is darker and graphic in comparison. It's not for the kiddies. If you like the early 90s style of animation then this will fit right in as DCS did. Both are full of demons and monsters and has the "must save humanity" vibe.
These are both sports anime that focuses a lot on triumphing over difficult odds. The characters in Princess Nine seem overall a little stronger than in Battle Athletes when it comes to confidence.
They both give depictions of what it was like after WWII in Japan. Grave of the Fireflies gives the opinion more after the war was nearing it's end while Barefoot Gen gives perspective of both during and after the war.