Scottish Ballet won for A Streetcar Named Desire and Scottish Opera and Music Theatre Wales won for Ghost Patrol in the opera award.
Julie Walters, 63, was honoured with an outstanding achievement award to recognise an acting career spanning almost four decades.
Other winners included the Olympic cauldron which was given the visual arts award, while BBC2's spoof series about preparations for last summer's sporting spectacle, Twenty Twelve, was named best comedy.
Actor Tom Hiddleston took the "breakthrough" award.
James Bond movie Skyfall, the most successful movie at the UK box office, took the best film prize.
Walters, seen in films such as Mamma Mia! and Shirley Valentine as well as TV comedies including Dinnerladies, was presented with her award by her frequent comedy partner Victoria Wood. The adaptation of Parade's End, starring Benedict Cumberbatch and Rebecca Hall, took the TV drama prize.
Hilary Mantel won the prize for literature. Her novel Bring Up The Bodies has already brought her a second Booker Prize and was Whitbread's Book Of The Year in January.
The event is screened on Sky Arts on Thursday.