Again as I told you before - you are speaking of the television series. Nobody can answer you comparing American Gods the television series and Anansi Boys the book - because that's comparing a television series and a novel. Comparing American Gods the novel and Anansi Boys the book is reasonable, but already American Gods the television series has barely anything to do with American Gods the book (I mean, while the first season was faithful in terms of tone, already they had heavily changed several characters - for example Mr. Nancy, Laura or Easter from the television series have NOTHING in common with the character from the original books). The plot holes, the filler, the confusion, it all comes from the show either badly or partially adapting what is in the novel. So yeah, if you want a good comparison, read the book first to know how both novels compare. But you can't compare a television series with a yet-unmade adaptation.
Second point: you still seem to hold the strange idea that Neil Gaiman was the man behind the television series. He was not. He was the man behind the novel. If you want to judge the quality of Neil Gaiman's work, go read the original book. Neil Gaiman did not write, did not direct and did not control the television series. He even clarified it once again on his personal Tumblr right here if you still don't believe me:
https://neil-gaiman.tumblr.com/post/673323364701569024/i-mean-this-respectfully-but-it-seems-you-are
On the show, Neil Gaiman was mostly an advice-power, a suggestion guy. But when it came to decisions, it was not his sled, and he even had to go to huge lengths to insist to some points (if you don't know, when Fuller and Green the makers of season 1 wanted for Shadow to have sex with Audrey, Gaiman had to threaten with throwing himself under a bus to convince them to not do that).
So by watching American Gods you were not disappointed by Neil Gaiman, you were disappointed by first Fuller and Green (season 1), then by Jesse Alexander (the beginning of season 2) and Chris Byrne/Lisa Kussner (the rest of season 2). If you had read the book and not liked it, you would have been disappointed by Neil Gaiman - but since the show is not a faithful adaptation of the novel as a whole, you really can't say you are giving "Neil Gaiman a second chance". You aren't even giving a second chance to the team of American Gods the television show - because the new Anansi Boys show is made by very different people, a very different team, and has nothing to do with American Gods the television show.
All that being said, I can try to answer your question as best as I can. Will you give a "second chance" to the character of Mr. Nancy? Probably not, because Neil Gaiman explained that the characte of Mr. Nancy from "Anansi Boys" will be the character from the novels, not the version created by Fuller and Green for the show. So no tall, handsome guy, and no angry rants or god of rebellion and rage. Mr. Nancy in both novels was rather a small cheerful old man, who likes to crack dirty and funny jokes, the kind of guy with always a smile, a trick and a good prank up his sleeve (even though in Anansi Boys one explores how this personality, while charming for his friends and allies like in American Gods, can be a bit more negative when it affects his direct family, aka his son in Anansi Boys). So yeah, on that point the characters will be radically different.
While I can't tell how they are going to adapt the novel, if I compare American Gods (the novel) and Anansi Boys (the novel), the two stories are indeed very different. Anansi Boys was not created as a complement or spin-off of AG, in fact if I recall Anansi Boys was written first and then AG in a second time. Anansi Boys is not as serious as American Gods, though it also becomes just as dark if not darker in several aspects. Anansi Boys begins mostly as an humoristic book (though, no pun intended, the genre is rather a sort of dark comedy, as it depicts a normal man, stuck in a boring and not-too-pleasant life, being faced with extravagant supernatural relatives, strange witchcraft invoking gods from ancient times, and cosmic threats of all sorts). American Gods was much more serious in tone.
American Gods was a story with a huge number of characters, a supernatural and philosophical roadtrip with a lot of oniric and mysterious moments, deep considerations on the nature of religion, America, and overall very tied to the culture and story of the United-States. It was also a sad story about the decrepitude, things being forgotten, about mighty and powerful people getting old and sick and just dying, about the conflicts of old vs new, religion and technology, etc, etc...
Anansi Boys is much less reflexive. You don't have big reflexions on religion, nationality, etc... It is not a story tied to a country or a given place (as the main characters oscillate between three different countries if I recall), it is rather a story centered around the characters - a really character-driven story. Due to this smaller scale and greater focus on characters, it is much more of a "fantasy" story so to speak, in the sense of "urban fantasy". In fact you can say this story has more in common with some of Gaiman's other works like Coraline or Good Omens, where American Gods was more in the lines of Stardust.
It is not a question of if Anansi Boys is "better written" than American Gods. Because the two were written by the same guy, around the same time, and I can't even answer you on that because you did not read the novel so you don't have any idea if American Gods was written in a good or bad way (it is like judging Tolkien's writing style by looking at the Lord of the Rings movie, it is impossible as reading the book and watching the movie is two heavily different experiences). I would say the main difference between the two is the tone, focus and orientation of the story. One is an epic, sad, serious story of road-trip and culture exploration ; the other is a urban fantasy and dark comedy about a guy's life turned upside-down by supernatural powers of all sorts. Well in fact you could say that both stories are about a regular man whose life is turned upside-down by supernatural powers and the discovery of another world below our own (but so is Stardust, and Neverwhere, and yet each time Neil Gaiman produces something different entirely).