Hugo's Tragic Beginnings
In the manga, Hugo met Alita after she got her Berserker body and became a weapon of mass destruction. They fell in love, and she eventually tried to help him earn credits so they could move to the Sky City, but Motorball wasn't a part of their life. He stuck to scrapping and selling robot parts to Vector while she remained a bounty hunter. We'd eventually find out Hugo's brother was sold out by his own wife years before, as he was trying to build a balloon to take them to Tiphares, and after their deaths, Hugo decided to follow his brother's dream.
The film follows most of this beat, although Hugo (Keean Johnson) meets Alita before she's upgraded to Berserker mode, right after Dyson brings her back to life. The biggest change is how Motorball becomes a big part of their livelihoods. Also, there's no tragic family background for Hugo; he simply wants to become one of Zalem's elite. In the film, Hugo gets gutted by Ed Skrein's Zapan, whereas in the manga it was the hunter called Clive Lee, who had a lifelong vendetta against the boy's family. Daisuke gave him his robotic body in the manga, but in the movie, Chiren also helps save his life. Sadly, in both instances, Hugo would perish trying to use his new form to climb to the Sky City.
Alita's Overall Destiny
Most of the changes are with Alita herself. In the manga, she's named after Daisuke's dead cat, not his daughter. As for the Berserker armor, Daisuke builds it for her, repurposing a suit that was made to turn a human into a weapon, as opposed to the film which retcons it as a suit Alita finds that's meant for her line of robots, a line used by the United Republic of Mars to wage war on Zalem 300 years ago.
In terms of her villains, in the manga, Makaku is the person who slices her up which allows her Berserker upgrade, but on screen it's Jackie Earle Haley's Grewishka. As mentioned, the manga doesn't have her trying to turn all the Hunter-Warriors into a rebellion against Vector like the movie does. What's also noteworthy is in the manga, her main enemy, Nova, isn't a technopath hidden in the Sky City. He's right down there, exiled with everyone else, whereas Edward Norton's character is painted as a demigod in the film version, high above in Zalem.
As for Motorball, in the manga Alita uses it to get over Hugo's death but on screen, it's her ticket to Zalem and to killing Nova, Vector's boss.
Directed by Robert Rodriguez, Alita: Battle Angel stars Rosa Salazar, Christoph Waltz, Jennifer Connelly, Mahershala Ali, Ed Skrein, Jackie Earle Haley, Keean Johnson, Michelle Rodriguez, Lana Condor and Eiza González. It's in theaters now.