A lot of rationalizations in this thread...
Ether was the best track in that battle, but it doesn't even matter. Even if Takeover had been better musically or even if Jay had another 5 songs that were musically better than Ether, Jay still lost because of the impact Ether had on him.
This was more than just a contest of who had the better music, it was a strategic battle straight out of Sun Tzu. And in the end, Nas just outmaneuvered and outplayed Jay.
Jay thought he had the advantage so he hit first. He thought Nas was done anyway and he wanted to take credit for ending him, and also to get revenge because Nas didn't extend him the respect he thought he deserved.
Nas was hit hard, but he remained calm. He didn't rush into responding like Jay later did with Superugly. Nas bided his time, got his shyt together and came out not only with his best punch musically, but with a full blown psychological attack on Jay. Unlike Nas, Jay didn't know how to act. The truth is that Ether broke him. He went from being on top of the world one day to sounding like a rape victim on Hot 97 the next.
Instead of doing what Nas did, Jay rushed out into damage control mode and put out half-baked shyt like Superugly and the track where he called himself "European Hov"(

). And the fans didn't miss that.
That was where the battle was lost. Everyone started riding with Nas after that, not because Ether was
that much better musically than Takeover(it wasn't), but because Jay acted like the loser and Nas acted like the winner. Even people in Jay's own camp could see that he lost and told him so.
People see what you let them see, and when they looked at Nas they saw a confident dude who acted like he won, and when they looked at Jay they saw an insecure, broken dude sounding like "d-d-did I warrant that?

", not like his usual cocky and aggressive self.
Even a year later that demeanor still hadn't changed:
- on Last real nikka alive Nas had the attitude of "ok it's over, I won, let me tell all of you what happened"
- on Blueprint 2 Jay
still acted inferior, he was still campaigning for the people to ride with him("but but I donate alot of money, how much does Nas give?") and trying to save face("even in defeat...")
***
I'm a Nas stan but from my POV, while Nas' music was better, it wasn't
that much better than Jay's. If you compare Ether + Stillmatic freestyle + random subliminal jabs vs Takeover + Superugly + random subliminal jabs, Nas won, but not by a lot. I'd say it was 60% vs 40% in Nas' favor.
But the real 'war' was fought the way I described above, and Nas won. Jay-s hundreds of millions or his pretty wife don't retroactively change that.