Mahou Shoujo Lyrical Nanoha ViVid

Both series focus on a small group of characters, primarily young girls, fighting alongside and against each other in organized tournaments that are popular spectator sports. The battles in Angelic Layer are fought with electronic dolls that the competitors customize themselves and control with their thoughts, while the competitors in Nanoha Vivid are engaging in actual physical and magical combat, but both series share common themes like characters wanting to grow and become stronger, bonding with their opponents through the shared experience of competition, age and size being no barriers to success, and learning to trust themselves and their own capabilities in order to succeed. 

Both anime feature girls who battle each other in a major tournament. MSLN Vivid involves the magical girl genre, while Venus Project: Climax is an idol tournament.  

-Both are light-hearted (when compared to their parent stories) magical girl anime -Both main characters are 10 year old girls with a magical companion -Nanoha Vivid has more sci-fi elements while Prisma Illya is more supernatural 

Seriously, ViVid feels much more like YuriOnMahjong rather than other Nanohas out there, so, if you liked one, you definitely should check out the other.