Kidou Tenshi Angelic Layer, Busou Shinki Moon Angel Recommendations
Both shows are about 15 cm (roughly) tall robots and some form of tournament battles. You get to customize and train your companion while fighting against various kinds of opponents in normal or tournament style battles. Both main characters start in a near similar fashion working their way to the top. I find this to be the most appropriate Anime to recommend when watching Moon Angel.
Main difference however is ammunition is live and Shinki's have full A.I when compared with "Angel" who need platforms to battle. Rest is similar.
Both animes are about playing games using mechanical dolls that they customized themselves, whether it's for fun or for various tournaments.
but how they play the game, and the game's backgrounds are different
Both include small robots and boys who control them in competitions versus different opponents.