While A Girl Like Me is much lighter than The Rebel Princess, both stories are focus around the strength of the female lead. Both FLs are close family to the emperor who tends to favour them as a young girl in the family. Emperor indulges both FLs to choose their spouse, in both cases they actually end up choosing someone strategically but it is a love match. Both shows are about navigating political schemes which they just get caught up in. One has a mother who is a princess and the other a grandmother who is a princess. One has a ML who is the army general with military power and the other a close advisor to the emperor with political power.
Girl Like Me has a romcom feel whilst Princess has a dramatic feel.

This drama is very similar and feel and also storyline like Skate into love. The leads have a similar relationship of not getting along at first but when they do get together (relatively early on) they have other struggles to get through together. A team of friends around them that add to the youthful hope that both Dramas convey.

While watching both these romances simultaneously I get the same "feel" from both of them.
The FLs are both smart, hard-working and assistants tot he ML
The MLs are both aloof and have the same type of appearance (physically)
There is also a more direct approach from the FL in both dramas to their feelings.

These dramas feel similar because of the male lead in both:
Both MLs are professors but not just professors... they both have an aloof demeanour but are logical and unsure of how to handle love, but at the same time they are pragmatic in their approach. I am not finished Be With You but it looks like it will follow a similar evolution of love and commitment.

ML is superman archetype, loner,
FL curious and brave despite childhood trauma
Both support justice in their own way , ML seemingly hesitant to get involved in worldly affairs
Dark but witty dialogue to create balance
Intriguing investigative adventure with romance at its core
****Please note these parallels are made after only two episodes -rest of episodes may alter this opinion.

-supportive ML
-both leads end up with same interest
-light/low angst
-sports, competition
-teamwork

-school based
-ML supportive of the FL's dreams
-low angst
-faithful ML
-ML is popular
-light and lovely
-both MLs are quite pleasing to look at
-both MLs have a cheeky attitude towards the FL

-cohabitation with ML
-friendship/ interests with SL
-ML /SL brothers
-brothers have old relationship issues with love for same person (father/girl)

Both leads knew each other in school drifted apart. Paths crossed as adults. ML clearly like FL who through some misunderstanding thinks the opposite. ML chooses to work independently without communication and support the FL.
Same light vibe. Watching these together while airing gives off the exact same fun vibes. Chemistry between leads is also very good and similar.

both are court conspiracy and romeo and juliet -esque in nature, FL saved but rest of family killed, ML's family connected to this...

The male lead has an attitude similar to the ML in Joy of life. Similar approach to romance, loyalty etc. Also has a childhood that is mysterious.

-hidden identities
-lost families
-strong female lead
-romantic partners working together To solve problems
- setting and of course the male lead
-overall look and feel very similar