It kinda depends what you are looking for. Gameplay-wise, Engage is so much better than Three Houses. The pacing is better, the maps are better, the objectives are better.
Story, characters and world-building are all better in Three Houses.
This exactly. I'm replaying Engage and everything you said is spot on.
I thought the Emblems were going to be cringey fanservice crap, but they're actually fun to utilize.