Kingdom Come wasn't considered whack because no one wanted to hear a mature Jay. It was whack because them beats was whack and his flow was corny. It was a corny album.
As for classics, Nas has one official classic in my book and that's Illmatic. Jay-Z has arguably two and that's Reasonable Doubt and Blueprint. But yet (*SHOCKER*) Nas is still my favorite rapper. Let me tell you why.
Outside of rap message boards full of stans and groupies, no one talks about Jay-Z and Nas having 5-11 classic albums. Shit is just silly. No artist on the planet has that many, especially not rappers Jay-Z and Nas (go ahead and run the gamut of Michael Jackson, James Brown, Miles Davis, and the Beatles and you still won't get there).
Nas has 5 great albums, there's a difference (great album doesn't equal classic). When you read journalists and critics refer to classic albums, they mean albums that are musically perfect, have stood the test of time, and had significant cultural, artistic, and/or social influence. Only three albums really fit the bill in the case of Nas and Jay-Z on this score and that's Illmatic, Reasonable Doubt, and Blueprint. Although Jay has two classics, neither of those albums are quite as great as Illmatic. They're virtually perfect albums, but don't reach the level of greatness of Illmatic (this is consistent with what most critics and journalists think).
It Was Written can't be classic because not every song on that album is perfect ("Nas Is Coming") and it didn't shape a sound so much as borrow one (from Raekwon's classic LP Only Built 4 Cuban Linx). Admittedly, nearly every song is a banger and Nas is a lyrical beast on that album. It went from the initial backlash and mixed reactions when it was released off the the heels of Illmatic for its obviously more commercial sound to years later being acknowledged as a great album and containing some of his best work. That's all a given, but again, not every great album an artist makes should be called a classic.
Stillmatic is not a classic because it has at least one or two weak/subpar/average tracks on it ("Braveheart Party"). It's also not a very influential album, even if it's a very important album for Nas. It's a great comeback album with an artist at the top of his game. The same can be said for both The Black Album and American Gangster. Great albums overall, but not perfect, and certainly not influential (and haven't withstood the test of time).
The Lost Tapes ain't a classic because for one, it's not an official solo album. And two, it's not a very artistically or culturally significant album that has been highly publicized (its quiet release had no real impact on the game). Rather it's a collection of classic cuts unfortunately omitted from two Nas solo LPs. It's simply a wonderful little album of lost gems that's like a gift to the true Hip-Hop head and Nas fan.
As for great albums, Nas has (IMO) five: Illmatic, It Was Written, The Lost Tapes, Stillmatic, and Life Is Good.
Jay has four: Reasonable Doubt, Blueprint, The Black Album, and American Gangster.
If we're counting collaboration albums, in my view, Distant Relatives and Watch the Throne are pretty much on par with each other.
It would seem then that Nas has more great albums, but Jay arguably has one more classic album than Nas. I still prefer Nas because (1) he has more great albums than Jay, (2) he's had an overall more consistent and balanced career artistically as he's still making great solo music and he never fell off lyrically or with his flow like Jay (i.e. Kingdom Come era whisper whining), (3) I simply relate to his music more and find him a superior and more influential lyricist and (4) Illmatic is still better than anything Jay-Z has ever made (and most critics agree with me).
Most Nas stans couldn't fathom giving Jay the kind of nods and concessions I have in this post, but I don't consider myself a Nas stan, even though he's my favorite rapper. I consider myself a Hip-Hop fan first and foremost and must give credit where credit is due. I simply feel Jay as a matter of fact has one more classic (though lesser classic) album than Nas given Blueprint's artistic influence on the game, but overall I prefer Nas' career and music. I think the closest you can get to an objective opinion on this matter is to see how well your opinion matches up with or approximates what most professional critics would say. Otherwise, there are no standards, and it's purely subjective, so there's no point in arguing about anything.