Sousei no Onmyouji and Ao no Exorcist focuses on the main characters and their fate to become exorcists. Their motivations aren't similar but they both face difficult challenges on their path to becoming an exorcist. Throughout both series, we also learn much more about the characters including their past. There is also a consistent amount of supernatural themes that relates with demons, apparitions, and exorcism. Sousei no Onmyouji is also known for its romance that is subtly developed while Ao no Exorcist focuses more on shounen aspects.
Sousei no Onmyouji is similar to Ao no Exorcist due to how the plot revolves around exorcists/onmyouji fighting impurities/demons from separate dimensions. Both main characters have powers connecting them to the same demons they fight and their personalities are similar as well.
They are both focusing on becoming the stronger exorcist and achieving an incredible goal both man characters Rin and Rokuro have a sad background , Rin lost his parents and Fujimoto , on the other hand Rokuro lost all his friends durins the hinatsuki tragedy and they both unlocking their powers while times passes and not overnight
Both are action shounen manga that involves demons and humans. Human can turn into demons by being "infected". Both have MCs that join an organization to fight these demons. Both have a female ally to the MC. There's also a ranking system in both human and demon power levels.
The time period is probably the only big difference.
-Both are set in a high school for powerful figures in their own world, Boku no Hero Academia has the school for heroes and Sousei no Onmyouji has the school for Onmyouji.
-Both have a powerful male lead who is being mentored by some of the most powerful people in their worlds, Boku no Hero Academia has all might and the teachers of UA while Sousei no Onmyouji has the twelve guardians and the head Onmyouji.
In both series, the main protagonist is part of of family generation with connections to supernatural forces. Their life changes drastically after the arrival of a girl as they embarks on their destined role. Both series contains a lot of supernatural phenomenons. As the story progresses, the main characters also gain new abilities to fight against powerful enemies. Both series' past also has strong influences with events in the present so expect the storytelling to have connections with certain characters. Recommended for fans of supernatural shounen.
Both involve spirits and forgetting or remembering their past
Spirit Circle is more of reincarnation while Sousei no Onmyouji is more of fighting evil spirits but if you like one them then you might like the other.
Soul Eater and Sousei no Onmyougi follows a different premise but both unites destiny with the main protagonists. The female protagonist is strong in their story and strives to improve themselves every day. There's also a similar personality with the main male protagonists as they share a complicated relationship with their partners. Both series has a lot of action, supernatural content, and a bit of mystery. There's also background story that connects the characters together. Recommended for fans of supernatural shounen.