So I LOVED Three Houses! That was my first tactical rpg and I spent hundreds of hours playing the different houses and meeting all the students and building them up into the unit you want.
The story in Engage really got cheesy.... not just linear but the vibe of Three Houses was just a much more mature story and the characters back story was more filled out or just the mechanics make you care more about them. There was cheese dialog but just sprinkled in a serious medeival fantasy drama. Engage is a cheese story in general.
ALSO the camera really bugs me in Engage, the angles were alot better and free in 3H. Very disappointed I have been anticipating this entry but find the dialog so cringe I can't get past chapter 10