This book should definitely be adapted into movies for the modern viewers, and I fancy there can be at least two different versions, depending on the targeted audience.
The R-rated version: The hero is a handsome, passionate prince with an uncontrollable temper, who attracts women everywhere and gets into fights (verbal and physical) with men. There would be plenty of scenes of sexual tension, seduction and violence (with blood spills and severed body parts). The main appeal, however, should still be the flawed hero himself, his humanity, his rise to greatness and tragic decline.
The ecclesiastical version: The hero is a proud, ambitious man, who, after he was used and disillusioned by the Russian high society to which he aspired, becomes a monk and strives for excellence in the service of God. Tolstoy provides an incisive portrayal of his internal conflicts, his lust, pride and emotional barrenness. His struggles and triumph over sexual temptations are compelling, but his spiritual burnout and subsequent downfall are even more poignant and instructive, considering how many church leaders today have fallen into the same trap.