Hard to say. True Grit isn't technically a remake as both versions are based off a novel, but the John Wayne version picked up Oscars in spite of being a loose adaptation of the book. The Academy aren't generally the best judges of movies -some members have 'fessed up to voting for films they haven't seen. A lot of them are coffin dodgers who voted for the first version, so there may well be truth in that.
Yeah, the Cohens, Javier Bardem, Matt Damon and Jeff Bridges have all been honored in various categories in the past. I don't think it comes down exclusively to who is the most deserving winner in a given year... and it should, really. Geoffrey Rush came away empty-handed...but then he already earned a baldie for Shine.