The film is a prequel to 101 Dalmatians and follows Cruella de Vil from her roots as an orphaned urchin to an aspiring fashion designer determined to avenge her mother's death.
The Guardian said the film was "extremely entertaining".
But The Times called it "messy, flabby and confused".
The evil, dognapping character was a terrifying Disney icon when 1961's original animation 101 Dalmatians was released,
This latest film follows 1996's live-action version starring Glenn Close, and its sequel in 2000.
The film stars Dame Emma as Cruella's boss Baroness von Hellman, who runs prestigious London fashion house.
The Guardian's Peter Bradshaw described the two leading actors as "a sensational couple of Emmas".
"Together, they are the highly strung dysfunctional double-act that post-lockdown cinema didn't know it needed," he added in his four-star review.
However, he questioned the storyline, writing: "It's all extremely entertaining, although I do have to say that in these snowflakey days of emotional correctness and respect for animals, this movie rather fudges the whole question of Cruella actually wanting, now or in the future, to kill Dalmatians for their skins."
The original films were focused on Cruella's desire to murder Dalmatian puppies to use their fur for a coat.
The newspaper also welcomed seeing the film in a cinema, adding: "The big screen is surely the place to marvel at the film's digital recreation of London in the mid-70s."
But Kevin Maher of The Times was less enthusiastic, saying Stone "just doesn't scare you".
He added Dame Emma occupies "the seething, screen-chewing, coat-swishing and giddily villainous archetype" by "channelling the deranged diva personal of the Glenn Close Cruella".
Maher said the origin story was "a vague attempt to spin the tale as an All About Eve for the superhero origins crowd" but that "the result, alas, is much more messy, flabby and confused".
Variety's Peter Debruge expressed relief that the film was "not another Maleficent", which was an origin story for Sleeping Beauty.
He said director Craig Gillespie "who brought a wicked edge to pop-culture redux I, Tonya a few years back, has rescued Cruella from the predictability of the earlier 101 Dalmatians remakes".
The Telegraph's Robbie Collin noted Gillespie is "big on toxic female rivalry" and was broadly positive. "As remakes and spin-offs go, this one's barking up the right tree," he said.
"The film only shows signs of strain when the time comes to push the plot over a hump... it feels at least 15 minutes too long, and gives itself too many loose ends to tie up as its climax approaches."
BBC Culture's Caryn James said there was "something hollow at the film's centre", and that it was "lukewarm style over substance - with a narrative that's not as bold as its design".
"This modern Cruella is a baddie who deserves our compassion," wrote Brian Viner in The Daily Mail, adding the film's creators "played down" the storyline about turning puppies into coats.
"Instead, the writers and Gillespie try to make their lead character vaguely sympathetic and her motivations understandable".
Viner likened Cruella to 2019's Joker, "another prequel that sought to explain how Batman's arch-enemy and super- villain emerged" adding that of course "one major difference is that this is a comedy aimed at children".
"Some youngsters might be befuddled by the plot, which could have stood a bit of muzzling," he said, while agreeing that the film's running time was "20 minutes too long".
But The Sun's Dulcie Pearce was fulsome in her praise, writing: "Cruella is packed full of energy, action, punchy performances, incredible style, delightful dogs and one of the best soundtracks in modern film."
"The styling and creativity is utterly breath-taking," she added. "tTe two Emmas' scenes together are so delicious I wished I could have another bite the moment they finished."
Cruella was the first major Hollywood film to get an in-person premiere in LA earlier this month, in the wake of coronavirus restrictions.
The film was released on Friday in cinemas and has also been made available on the Disney+ Premier Access platform, which requires a £19.99 payment in addition to the monthly subscription charge.