Bruce hardly ever sleeps, but he has a lot more difficulty with sleeping than Tim does. Deep-rooted insomnia. (And don't get me wrong, I think Tim might have bouts of insomnia, and constant nightmares, but I just think his body responds to that by shutting down at any moment he feels even remotely safe). He has a lot of guilt about taking up any time to do things for himself, even to fulfill basic needs like eating or sleeping. The weight never leaves his shoulders.
Babs doesn't sleep at all, but she runs on sugar and coffee, not so much energy drinks. She'll do it if she's desperate enough, but she won't like it.
Dick is an insomniac who will take spontaneous cat naps throughout the day sometimes, but mostly he's just exhausted. He has horrible nightmares, but he also hallucinates during the day sometimes so he can't really escape them if he tried.
Cass sleeps, but it's hard for her sometimes. She has too much energy and thoughts keeping her awake. And she fears the nightmares. A lot of times she wanders through the manor after patrol or finds her way back into the cave to punch a training dummy to smithereens. Stephanie can sometimes get her to take naps, but it only works if Stephanie is in the room/actively cuddling with her.
Jason is also a raging insomniac, but he still tries some nights. Mostly he just patrols when he can't sleep (he does not have a good work/life balance, but, then again, do any of them?). Sometimes his nightmare are similar to flashbacks and then cause him to have actual flashbacks when he wakes up from them, and sometimes they're just so distressing he can't go back to sleep, but either way, sleep is a losing battle most nights. He still tries, though. He's tired.
Stephanie is tired, with college homework and patrol, but she manages to get a few hours in here and there. She sometimes falls asleep in weird places, like the floor or on a table. She doesn't even care.
Tim is not an insomniac. He has no trouble falling asleep. That's the problem. He will just fall asleep places when he has meetings and missions to plan, spreadsheets and mission reports to fill out, market research to conduct, galas to prepare for, cases to work, and, occasionally friends to hang out with. He's completely overworked, overbooked, and dying inside, but he refuses to change—partially because he has no idea how. But, anyway, he has to constantly pump his system full of caffeine to actually finish his mile long checklist in a timely manner. He has this thermos filled with liquid death that he refills his never-ending supply of mugs with constantly. His family would be more worried if they weren't just as bad.
Duke doesn't sleep hardly at all, but has managed to fly under the radar due to his siblings more obviously problematic sleeping habits. He can just disappear if he doesn't want people to know he's still awake. He, like Tim, is just far too overbooked to get anything close to a decent amount of sleep. He has patrol/sometimes school during the day, night school/homework/figuring out cases during the night, and has to fit in spending time with Izzy and his friends in between. Sleep is low on the priority list.
Damian needs his sleep, no matter how much he will try to deny it. He can go without it—he wakes up early for school every day despite being on patrol most nights—but he suffers for it. Bruce has even resorted to limiting patrol to weekends except during emergencies and special occasions. And occasionally when Damian uses his puppy eyes. He's a night owl, preferring to sleep in as long as he can.