They both lost the battle but they won something even better. They realize that they respect and admire each other and that their friendship meant more to them than either one of them thought. There is no winner or loser here as far as the fight is concerned. They are both battered and bloody and even though they slept through the night they don't have enough energy to move. Moving too much could cause them to bleed to death.
Sasuke was not admitting he lost the fight, he was saying Naruto's ideals were stronger than his own. That isolating himself and cutting off his feelings was not the right thing. That by finally acknowledging Naruto, he was acknowledging the part of himself that had feelings for Naruto and Team 7. I think that tear from him at the end was a tear of relief that he could finally accept that part of himself, realizing it wasn't a weakness.
He was quick to let Naruto know he was not going to accept everybody or everything. Which is as it should be because a touchy, feely Sasuke just wouldn't be right or true to who he really is. Naruto succeeded in ending the transmigration. Sasuke succeeded in letting Naruto know that while the two of them settled their differences, everything else is not taken care of and he's not willing to accept everything.
Bottom line is like true friends they will have agreements and disagreements, but probably none worth killing each other anymore since they both almost died and they both realize it now. Now hopefully Sakura and Kakashi will find them soon so Sakura can heal them enough to end IT. So please stop fighting over who won and who lost, they both won. Naruto got his friend back and Sasuke got rid of his hatred.
