Another thing that works for the animated effort is that nobody is chucked into the plot without a purpose. In BvS, it was all about throwing people together and killing time until Doomsday touched down. Gal Gadot's Wonder Woman stood out, yes, but you could easily tell this was to push Justice League into motion. Ultimately, her arrival took away from the Batman/Superman dynamic, overshadowing it. Snyder was simply trying to work in way too many moving parts.
Liu and Tucker, on the other hand, craft a world of inspirational superheroes, organically incorporating Justice Leaguers, as opposed to BvS which had brooding crimefighters who were bitter at every turn. Simple things, such as everyone offering Kal-El relationship advice with Lois, Wonder Woman being heartbroken over losing her friend, and so many other subtleties result in a story far more relatable and compelling than BvS.
Last but not least, The Death of Superman has heart. Superman's actually a beacon of light, something Snyder glossed over, with some of his scenes even framing Henry Cavill's Kal-El as a god people were worshipping. This took away from his humanity, something further exacerbated by his lack of compassion and empathy towards Ben Affleck's Dark Knight.
The touching and soulful scenes with Superman's number one fan, Bibbo Bibbowski, more or less sum this up. He adores Superman as he sees him as a man of the people, always smiling, whether he's stopping falling satellites from orbit or helping the old lady on the street. These little things set up the character as someone we care about, so that when the story eventually goes into Doomsday-mode, we care deeply for him and are rooting for a win.
BvS failed to take this approach, coming off cold and failing to paint the Man of Steel as someone virtuous in our eyes. This is why the audience didn't feel anguish at the end when he died, versus what viewers felt when Thanos' snap killed half the galaxy. As Bibbo mourns the character at the end, it embodies exactly what The Death of Superman was trying to achieve. Just like the DC filmverse, we all know he's coming back but in this case, Liu and Tucker manage to truly make you feel the loss of the world's greatest hero. They do so by focusing more on the 'man' and less on the 'super' aspect of the character.