Sherlock was a bigger dick in the books, and a scarier well-meaning antagonist (runaway Enola is literally being hounded by debatably the greatest detective of all time, and he's normally the hero, but from this tilted point of view he's the bad guy, and yet he's unfamiliar family and Enola likes him more than she likes Mycroft, it's a delightful mix of light and dark), while Mycroft was less of a dick, and more just lazy. Sherlock and Mycroft in the books are explicitly not looking for their mother, since Sherlock deduced that she left of her own accord. There was no "mother is Sherlock's problem, and Enola is Mycroft's problem." Mycroft takes point with Enola's guardianship simply because he's the elder and his name is the one on all the paperwork. He's technically responsible, not maliciously motivated. Sherlock and Mycroft don't care why their mother left (and abruptly abandoned Enola), they're just "Eh, whatevs. It's mom. She's free spirited and never does what she's told. Her running away is like, the least surprising thing ever. If she doesn't want to be found, then she won't be found." They (just Sherlock, really) chase after Enola, because unlike their mother who is a capable adult making bad choices, Enola is a child in their care and therefore an incompetent. Enola (unlike their mother) "needs to be saved."
Mycroft in the book seemed to be far less concerned about "breaking" Enola's wild spirit than the fact that child-raising was suddenly dropped on him by his money-embezzling runaway mom, and he doesn't know anything about children (and even less about Enola), except that Enola has seemingly been raised badly, so he plans to have her shipped off to a boarding school where the professionals can deal with the problem (there was no creepy thing with the headmistress crushing on Mycroft). After Enola runs away, Sherlock and Mycroft are like "I think maybe this is our fault. It would seem that we suck as guardians."
It's the combination of Enola not wanting to be shipped off to boarding school (and Mycroft's refusal to listen to anything on the subject) AND Sherlock and Mycroft's refusal to conduct an investigation into their mother's disappearance which prompts Enola to run away from home. If the police can't do anything, and her brothers won't do anything, then it's up to Enola to find her mom and confirm her safety and get some much-deserved answers. And she can't do that from the apparent hell of boarding school.
And, those answers do not come, at least not in books one or two (of six). Enola did not witness her mom's terrorist cell meetings. Enola did not immediately find a karate instructor who is able but unwilling to provide answers or at least pass a message along. Enola has to work to find small clues (mostly wordgame puzzles) that might eventually lead her to her mother over an entire series.
And then, for the immediate mystery of the first book (the Missing Marquess), that whole mystery was basically different, aside from the presence of Tewksbury. In the book, Tewksbury was a runaway because his mom treated him like a dress-up doll, and he wanted a manly adventure. Then an uninvolved kidnapping ring took advantage of the runaway situation by claiming credit and trying to demand a ransom (for the missing kid they didn't have). Enola and Tewksbury didn't meet on the train, while dodging an assassin. They didn't romance. Tewksbury's grandma wasn't trying to kill him to change his vote. There was no politics, beyond Tewksbury's family being wealthy.
Enola's landlady didn't rat Enola out to the cops for the reward money. IIRC, the book-version landlady risked death by standing up to the local mafia and lying to their faces to protect Enola and Tewksbury. And Enola didn't let herself get captured by the police in an act of self-sacrifice, to save Tewksbury (from... the police?).
Since Enola never got caught in the books, she never went to that finishing school, and Sherlock never showed up to have a warm family moment with her, and Tewksbury never showed up to rescue her. (Book-Enola also never stole an automobile.)
After beating the armed-and-dangerous kidnappers, Enola walked Tewksbury right under Sherlock's nose as she brought him safely to the police station, so he could be returned to his overprotective mother, so she could get back to trying to find hers.
And one thing that the book placed some emphasis on was that Enola is no "mini Sherlock". Enola cannot do the things that Sherlock does, nobody can, but Enola is gifted in her own ways.
