Shinji renounced the world where all hearts had melted into one and accepted each other unconditionally. His desire to live with 'others' -- other hearts that would sometimes reject him, even deny him. That is why the first thing he did after coming to his senses was to place his hands around Asuka's neck. To feel the existence of an 'other'. To confirm rejection.
That was from a official Evangelion card game.
But Asuka didn't reject Shinji she caressed him. Asuka caressing Shinji means that acceptance also still exists, even when all the hearts are separated.
The ending is definitely not 'And Shinji and Asuka both lived happliy ever after' and besides it's impossible to be happy forever but the ending does have hope for the characters to find happiness but in order to obtain it they must pursue it.
