I looked into this recently and basically Takeover vs Ether comes down to both the lyricism/musicality of both songs and the points both songs make.
Takeover is a very pounding and energetic track musically, and the Bowie voice samples are really great at pissing you off.
Jay has lots of good bars throughout. 1st verse is mostly bragging/metaphor. 2nd verse is mostly the same but he attacks Mobb Deep. 3rd verse is a pretty dense attack on Nas, and 4th verse is more bragging/wordplay.
Jay’s main points are 1. ROC is the most commercially successful clique in NY
2. Mobb Deep are fake thugs because Prodigy was a dancer as a kid (same applies to Tupac)
3. Nas has become irrelevant after the failures of IWW, I Am and Nastradamus and Illmatic was his only good album (about half of hiphop fans believe this)
and he was outrapped by Horse on Oochie Wally
4. Nas is a fake thug since Jay-Z brandished a Tec-9 on tour with him back in the late 80s/early 90s and Nas hasn’t done gangster stuff like Jay-Z
5. Jay-Z released more commercially successful albums starting from 1996 than Nas has released albums that Jay-Z likes since his first feature in 1991 (even though Jay-Z’s first feature is even earlier on Hawaiian Sophie)
6. Jay-Z fucked Nas' girlfriend/baby mama
Some of these points are obfuscations of the truth but 1 and 6 are pretty damning.
Ether has a less-polished beat but is still very iconic. Nas cleverly flips Jay’s interlude on U Don’t Know for the hook.
Nas is also very on point lyrically. All three verses involve both announcing his comeback and going after exclusively Jay-Z and ROC
Nas' main points are 1. It’s ridiculous Jay is attacking him since Jay loves Nas' style, seen by him changing his rapping style post-Illmatic, sampling his voice, and referencing Nas and the firm in his lyrics.
2. Jay-Z is disrespecting hiphop culture by calling himself god (Jay-Hova) and claiming he is better than Pac and Biggie
3. Jay-Z is unoriginal. He took his name from Jaz-O, and took the album title “The Blueprint” from KRS-One. (Granted Nas was also inspired by Rakim/Kool G Rap/others and was influenced by Biggie and Pac as well)
4. Jay-Z has corny lyrics (Tae-bo)
5. Jay-Z found a lot of commercial success from misogynistic radio singles (Nas has You Owe Me, Big Girl, and Oochie Wally but Jay-Z has a few more than him)
6. Jay-Z is ugly
7. Jay-Z has been outrapped by Beanie Siegel and Eminem on Renegade (I think they were both good on Renegade)
etc
Some people criticize Ether for lots of filler bars/namecalling but it’s believed that these were replacements for more controversial insults that the label wouldn’t allow, like saying Jay-Z should have died in the plane crash instead of Aaliyah and a story about Terror Squad killing Jay-Z with shotguns.
Sorry for the wall of text. Both are great diss tracks but if you’re a Jay-Z fan and not a Nas fan you probably wouldn’t care about most of Nas' points and think Jay-Z won since he did fuck Nas' baby mama and was a more “real” gangster than Nas.
If you’re Nas fan who doesn’t like Jay-Z’s output from 1996-2001 then you’d think Ether would be the far better diss and ignore the excessive namecalling.
The final vote was only 52% Nas so either opinion is understandable. The beef was great for both rappers' careers