ITV's Quiz and The Nest on BBC One both attracted healthy ratings and glowing reviews on Easter Monday.
Quiz, which is based on the Who Wants To Be a Millionaire? coughing scandal, was "the most entertaining thing ITV has done in ages", one critic said.
The first episode of Quiz was seen live by an average audience of 5.3 million.
The Nest, which saw a young girl with a troubled past become a surrogate to a rich couple, was hailed as "seriously gripping TV" after its finale.
The last episode attracted 4.7 million viewers. Both dramas were beaten in Monday's ratings by news bulletins and soap operas, however.
Coronation Street won the night for ITV with six million viewers, while EastEnders was watched by 4.8 million on BBC One. The overnight figures do not include catch-up, so the final ratings are likely to be significantly higher.
Quiz tells the story of Major Charles Ingram, a Who Wants To Be A Millionaire? contestant who was convicted in 2003 with wife Diana of cheating his way to the jackpot with the help of an accomplice who coughed when the correct answers were read out.
The Independent's Ed Cumming described it as "a brilliant, big-hearted romp through one of the great British scandals of the century" in his five-star review.
"Quiz is a belter," agreed Anita Singh in The Telegraph. "It takes you on a story you think you know, fills it with you've-got-to-be-kidding moments, gives it pathos and laughs and Michael Sheen as Chris Tarrant in Oompa-loompa orange foundation.
"It's the most entertaining thing ITV has done in ages, and fair play to them for green-lighting a show which makes ITV executives seem awful."
Lucy Mangan of The Guardian was more lukewarm, awarding the show three stars.
"The earnestness with which this is all treated may reflect accurately what goes into the genesis of a show, but to see it played straight is deeply offputting," she said.
"You long for a touch of W1A-type satire, a nod and a wink to leaven their awfulness and lighten the tone of a prelude to what surely cannot be considered the crime of the century."
Writing in the Daily Mail last week, Tarrant himself left little doubt about his own feelings towards Ingram.
"I have just one slight problem with Quiz. It suggests the Coughing Major Charles Ingram might possibly be innocent of fraud. And that is blatant nonsense."
As the first episode was broadcast on Monday evening, the presenter's son Toby praised Sheen's performance.
"Really enjoyed Quiz tonight, looking forward to the rest of it," he tweeted. "Michael Sheen as expected is brilliant as Dad. To be fair, he's so good he'd probably be convincing as my Norwegian auntie Tina."
Quiz went head-to-head with The Nest, which told the story of Kaya, who volunteers to be a surrogate for Dan and Emily Docherty.
Things become more complicated, however, when the couple learn of her troubled past.
Critics were largely positive about the show's conclusion, but some were not fully satisfied by the ending. "If truth be told, The Nest involved a bit of a cop-out," said Singh in The Telegraph.
But overall she concluded: "The series has been so good. As a drama, it kept us on our toes, and our sympathies constantly shifted."
'Seriously gripping TV'
Stylist's Kayleigh Dray noted: "Some have praised the BBC One show's ability to keep viewers guessing until the bitter end, while others have lambasted writers for piling too many plot twists into the hour-long finale.
"Whichever camp you fall into, though, there's no denying that it made for seriously gripping TV."
Scotland on Sunday's Aidan Smith said: "Apart from the final ten minutes when there was probably no avoiding the clutter of explanatory chat, Taylor kept all of her plates spinning, along with all of our emotions.
"Is there enough intrigue for a second series? I'd say so."