I have two disclaimers:
1) I'm a white male, so obviously my opinion in this debate is irrelevant. Nevertheless, I'm going to offer it anyway.
2) I've been a HUGE fan of Cornel West for ages. He's brilliant and I'm openly biased in his favor.

The dispute between Coates and West started with this article from West in response to Ta-Nehisi Coates’ book We Were Eight Years in Power.

Coates and I come from a great tradition of the black freedom struggle. He represents the neoliberal wing that sounds militant about white supremacy but renders black fightback invisible. This wing reaps the benefits of the neoliberal establishment that rewards silences on issues such as Wall Street greed or Israeli occupation of Palestinian lands and people.
The disagreement between Coates and me is clear: any analysis or vision of our world that omits the centrality of Wall Street power, US military policies, and the complex dynamics of class, gender, and sexuality in black America is too narrow and dangerously misleading. So it is with Ta-Nehisi Coates’ worldview.
...In short, Coates fetishizes white supremacy. He makes it almighty, magical and unremovable. What concerns me is his narrative of “defiance”. For Coates, defiance is narrowly aesthetic – a personal commitment to writing with no connection to collective action. It generates crocodile tears of neoliberals who have no intention of sharing power or giving up privilege.
When he honestly asks: “How do you defy a power that insists on claiming you?”, the answer should be clear: they claim you because you are silent on what is a threat to their order (especially Wall Street and war). You defy them when you threaten that order.

Yes! Yes! And Double Yes!
You should always be dubious of any political movement that doesn't threaten the existing power structure. Replacing whites and males with blacks and women in the corporate boardrooms and political offices without addressing the existing system of oppression is pointless.
In a separate interview, West make a more direct point about Coates' book title.

Yes. “We Were Eight Years in Power.” Who’s the “we”? When’s the last time he’s been through the ghetto, in the hoods, to the schools and indecent housing and mass unemployment? We were in power for eight years? My God. Maybe he and some of his friends might have been in power, but not poor working people.

That is why blacks are worse off economically after eight years of Obama.
Some of Coates' defenders have come out of the woodwork with particularly snide comments.

After all, he is a world-renowned academic busy saving the world.
...
West’s characterization of neoliberalism is opinionated but largely correct.
...
I hesitate to call West’s callouts a “beef” because Coates is seemingly disinterested in becoming Biggie to West’s Tupac-ish shenanigans. (And yes, they have risen to the level of “shenanigans” because, even in the merit-based part of West’s argument, there is an undeniable level of saltiness that extends past the text of Coates’ writing.)
...
Lost in West’s criticism of Coates is an insidious undercurrent that repeatedly asks, “Why does he talk about race so much?”

West has been fighting for blacks for longer than this a**hole has been alive, and he has the nerve to put words in his mouth? For shame.

Even in his conversation with The Root, West cast his criticism in more nuance, explaining that Coates was a “brilliant brother, and we’ve got much to learn from him.” But West continued:

I just don’t like talking about white supremacy independent of the empire and patriarchy, especially of class. I think that we can’t be pre-Du Bois. Du Bois taught us white supremacy is always to be viewed in relation to class patriarchy and empire and homophobia and transphobia. If you’re talking about white supremacy as if it’s up here, you end up acting as if it’s all-powerful because it looks like it’s winning all the time, it’s winning all the time.

But it is the extra shit that makes West look like Michael Jordan throwing marbles on the court while LeBron James is breaking away for another awe-inspiring dunk. And with West—God love his brilliant soul—there is always the extra shit. Always

Obviously West was throwing pearls before swine.
It's amazing how the people who talk about intersectionality in regards to race and gender, have so much problem seeing how class and empire are it's driving forces.

Unfortunately, Coates’ allegiance to Obama has produced an impoverished understanding of black history. He reveals this when he writes: “Ossie Davis famously eulogized Malcolm X as ‘our living, Black manhood’ and ‘our own Black shining prince.’ Only one man today could bear those twin honorifics: Barack Obama.”
This gross misunderstanding of who Malcolm X was – the greatest prophetic voice against the American Empire – and who Barack Obama is – the first black head of the American Empire – speaks volumes about Coates’ neoliberal view of the world.
Coates praises Obama as a “deeply moral human being” while remaining silent on the 563 drone strikes, the assassination of US citizens with no trial, the 26,171 bombs dropped on five Muslim-majority countries in 2016 and the 550 Palestinian children killed with US supported planes in 51 days, etc. He calls Obama “one of the greatest presidents in American history,” who for “eight years ... walked on ice and never fell.”

West says it more eloquently than I could. I would simply point out that this “deeply moral human being” bragged about his bombing seven countries and that he’s “really good at killing people”.

However, the best response to Coates' unconditional praise of Obama's moral character doesn't come from me, or even West. It comes from a black person living abroad.

It’s painful to us, in the global south, to see that American writers that we read assiduously, and take seriously, are not reading us. They are not listening when we say: “Please ask your president to stop killing us.” They appear to simply not see black and brown bodies beyond US borders.
...An unrealistic and ahistorical code has been invoked, of global solidarity among people of colour, to silence debate on the actual mass slaughter of black and brown bodies by the first black head of Empire. Gabeba Baderoon, South African professor of gender and African studies at Penn State University, calls this “the imperialism the US engenders, even in its citizens of colour”.

This response is both brilliant and tragic. There's nothing like American bombs falling on your village or town to cut through all the bullsh*t.
It is the ultimate takedown of Coates and his neoliberal defenders' worldview.