Busou Shinki Moon Angel

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. 

Very similar concept of boys using plastic models/figurines to be skanned by a battle system and then engage in a virtual battle that uses these models in a more realistic action. 

Although the premise and genre are different, when I watched Busou Shinki Moon Angel I was immediately reminded of Rozen Maiden. In both anime we have some kind of toy that approaches a hikikomori kid and somehow helps him socialize and build confidence. Shinku and Kaguya are also very similar in appearance (blue-eyed blondes with long hair) and the same is true for Jun and Tsubasa. They also have the master-servant relationship, though in Rozen Maiden it's much more complicated. 

Both shows fall into the 'Mecha Musume' genre of armored girls fighting, and although Busou Shinki plays it straight with robots and science rather magical powers if you are fans of girls in armor you might like Busou Shinki. 

IS and moon angel have similar battle suits  

Hoi Hoi San is a cute little insect "Exterminator".... Both are small angels with powerful weapons, if you like one, more likely will like the other as well. 

Does artificial intelligence exist? In Chobits, they are in a way looking for it, for it is considered the thing to achieve in programing. In Bosou Shinki Moon Angel, it is an issue of not a good thing, because they go against orders. 

Both are Mecha Musume shows, and even the main girl looks similar! 

Kids find toys and fight with them. The only big difference is that Busou Shinki takes itself significantly more seriously than Gunpla Builders does.