Britten's opera tends to see things in simpler terms. It portrays an Aschenbach who wants a richer form of sexual fulfillment, and who is hemmed in by the social conventions to which he subscribes. But Visconti's use of the Mahler Adagietto is perfect for what I take to be Aschenbach's sexual desire.
The classical allusions and the Platonic disquisitions on beauty are no longer a form of cover, but integral to Aschenbach's complex sexuality. Moreover, the wandering around Venice in pursuit of Tadzio isn't a prelude to some sexual contact for which Aschenbach is yearning.
We find in the novella a seamless interweaving of at least two narrative voices, one of which is that of an observer so sympathetic that his language appears to be Aschenbach's own, the other of which is superficially celebratory (except at the moment of moralistic condemnation) but undercuts Aschenbach by means of an ironic detachment.
To my mind, Death in Venice represents an enormous advance in Mann's literary development, not simply for the commonly appreciated reason that he crafted a superbly supple and elegant style, apparently well suited to the kind of prose Aschenbach is supposed to write.