Kishuku circles race vs race and Nisekoi is yakuza vs yakuza. Highschool students suppose having a childhood rivalry between protagonist and main love interest. Kishuku leans more of the "Romeo and Juliet" scenario while Nisekoi follows a different picture book.
Both are romance anime that use the childhood love trope. The parties of both romances are rivals. In Nisekoi, Raku is apart of the yakuza, while Chitoge is apart of a gangster mob. In Kishuku Gakkou no Juliet, Romio is apart of the Black Dogs, while Juliet is apart of the White Cats. Both are also school based.
However, Nisekoi is a harem, and is more comedy. Kishuku Gakkou no Juliet is not a harem, and is more action.
Both shows are romance comedy shows whose setup is a nod to the original story of Romeo and Juliet. The hero and heroine in both shows are from rivaling groups, and there's the typical high school setting. However, Nisekoi utilizes a lot more generic tropes than Kishuku Gakkou Juliet. Also, the former has more of a harem aspect to it, while the latter is more shounen and action-based with fierce competitions between the two parties.
When I was watching Boarding school Juliet, I could not help but remember Nisekoi. Nisekoi is a romance comedy that circles a similar plot. The main characters of Nisekoi are high school students Raku Ichijo, the son of a leader in the yakuza faction Shuei-Gumi, and Chitoge Kirisaki, the daughter of a boss in a rival gang known as Beehive. However, Nisekoi is a harem and holds a question who Raku ends up with.
Both loosely based on Romeo and Juliet by William Shakespeare
Show rivalry between clans and the star-crossed lovers hiding their love from their clans.
Kishuku Gakkou no Juliet is more on modern mixed with medieval and romantic comedy while Romeo x Juliet is more on fantasy and tragedy.
Black Doggy Dorm - Montague Family and White Cat Dorm - Capulet Family
Romio Inuzaka - Romeo Montague and Juliet Persia - Juliet Capulet
Juliet is more of a fighter.
Both shows focus on 2 characters who are in love with each other, however, due to social classes they are unable to be with each other. As a result, they secretly hide the fact that they are a couple from their peers
Both animes are romcoms, but Mayo Chiki focuses more on the "romance" part and has a lot more emphasis on slowly building upon a story.
If you like romcoms in general, you'll enjoy Mayo Chiki a lot. (it's my personal favorite)