I'm kinda sick of people saying you can't have both.
My favorite superhero series are Batman:TAS and The Brave and the Bold, because they managed to do exactly that, each with an emphasis on one of these aspects.
TAS gave us gritty Batman, with a somber, kinda bleak world and devastating storylines (like the one where Penguin reforms only to be rejected by everybody), while still being entertaining and funny (like the Ivy/Harley storyline, that still has a serious aspect, what with the abusive boyfriend side of the story).
Case in point
tB&tB gave us the exact opposite: a silver age homage that was completely hilarious (NPH as the Music Meister anyone?) but also had more serious moment like the Starro storyline and was even downright depressing at times: I'll never not cry at the death of Ted Kord.
Seriously, he just was the perfect BFF for Batman,
and it only took them two minutes to make us realize that.
Yes you can have both, but it takes good writers who love what they do and know what they're doing. So I guess we're not going to see this become the majority of superhero movies anytime soon.
Also, we need more tB&tB. It ended at the right time and the last episode was perfect, but still, I don't care, I want more goddammit.
"Nobody exists on purpose. Nobody belongs anywhere. Everybody’s gonna die. Come watch TV?"
"I'll die soon. But the last twenty minutes have been the best years of my life."