both manga have: handsome/rich/popular boy who falls in love with a "plain" unpopular girl who doesn't care much about clothes, and they aren't like the other fan-girls of the popular boy in both manga. Also: both boys are perverts and have somewhat nasty attitude in their private life
Both series involve a romantic relationship developing between an older woman and a younger man. In both series, also, the main woman is torn between love and her career at some point. Both are good series, with Kimi wa Petto being the better of the two.
Even if they're from different time and different manga waves, they have in common the kind of relationship between a middle-class japanese girls and royal european guys and, of course, the girls have to face a lot of difficulties on their way to happiness.
Both mangas are similar in a way that the girl ends up with someone who is rich.
Hana ni Arashi = girl ends up with the sole billionaire heir.
1/2 Prince = girl ends up with a Prince of a foreign country.
Well 1/2 Prince is longer compared to Hana ni Arashi and is somewhat smutty. I prefer Hana ni Arashi because of how cool the main guy is.
Both mangas involve the female leads who are reluctant to admit their feelings towards the main guys. Although 'It's Not Like That, Darling' takes a more comedic approach as opposed to 'Private Prince'. Both mangas are for mature readers.
Girl becomes involved in a relatiionship with someone of a higher status, facing many problems along the way to make the relationship recognised by those around them. Private Prince is much more smuttier though.