I also prefer trash of counts tbh, I love cale too damn much, he is so lovable and I really love the dynamics. I'm a softie and a sucker for sweet and heartwarming stuff.
And also in TBATE I dropped it after his confession to his parents about his true identity. It broke my heart so much that I cannot bear myself to continue reading it.
What I also noticed is that the few female characters in Trash Count are less sexualized/gendered than in TBATE. And they haven't fall in love with Cale, Thank God.
Generally I get the feeling that the characters in Trash Count have their own agency despite being "drawn" to Cale.
When I read TBATE everything is more focused and centered around Arthur who gets admired by everyone and how strong he gets by demonstrating his power growth...

The difference/comparison between "The beginning after the end" and "Trash of the Count's Family"....
Because TBATE keeps popping up in online comic websites.
I read many chapters and spoilers from NovelUpdate/Wikia about the story of Arthur Leywin.
I strangely relate more to Cale who is an intelligent mysterious schemer but prefers being in the background and having a comfortable leisure lifestyle; than Arthur who was in his first life a struggling orphan becoming a King/the strongest after losing his close ones and training for vengeance...
To be honest, I feel more comfortable about Cale, his worldbuilding + logic and people.
I think what I personally dislike about the world of Arthur/King Grey is the overdramatic tone, shonen trope vibes and its politics.
Correct me, if I am wrong but I get the impression that TBATE is more convential masculine, hierachal and pro monarchy.
I like to hear your arguments. To be clear, this is not about trashing the popular "The beginning after the end" but collecting other arguments why I and others prefer Trash Count.