Leigh and Minghella were nominated for best screenplay, with Leigh an early favourite for his story about the comically strained relationship between Gilbert and Sullivan.
Woman in Gold is released in cinemas next month, but at its premiere in Berlin the Austrian reviewers were generous about its portrayal of a national reluctance to face the art crimes of the past, according to playwright Alexi Kaye Campbell, who wrote the screenplay.
The choice between the two men for best original screenplay offers Academy members a unique opportunity to make a statement about movie violence, should they so desire, although there's not as much daylight between them as you might think.
A sizeable critical smash, it was nominated for five Oscars and the film-maker also took home the prize for best original screenplay last month.
The London Critics' Circle gave him best film and best original screenplay.
Many had predicted recognition for Whiplash's editing and best supporting actor (JK Simmons), but Damien Chazelle's taut drama about a ferocious drum teacher also scored best picture, best sound editing and best adapted screenplay nominations.
But there was nothing for Timothy Spall's performance, nor for Mike Leigh's direction or screenplay.
Rival scientist biopic The Theory of Everything took five nominations, including one for best picture, one for each of its leads – Felicity Jones and Eddie Redmayne - one for music and another for adapted screenplay.
Morgan, whose other work includes the screenplay for Margaret Thatcher biopic The Iron Lady, won the award for writing in a mini-series or movie.
Nominated for five Oscars, including a nod for the Pulp Fiction director's original screenplay, the film has been widely praised by critics.
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