So I just finished my 3 playthroughs with BL, BE & GD and unfortunately had read this with Golden Deer being my final playthrough. I still wanted to know more about what the main differences are and got some of it from this post, but I think I was still curious enough to get the full picture. There's a pretty solid video on youtube "Three Houses the Movie: Church Path" if you skip to the middle of it and just watch the dialogue & cutscenes it becomes super clear that it is nearly identical as OP says. I'll post my additions to the spoilers below of the differences I had found between GD and church.
*SPOILERS for GD route are also included in here.
Anyways - I hope this gives a better idea of what happens between the two. But seriously if you've done GD - SKIP this route. GD is a much better route to play through information and plot wise.