I must confess I have never read any book of the Terry Pratchett’s Discworld. And for the time being I cannot confirm to do so. Though I am familiar with Neil Gaiman’s writing which sometimes fascinates me. Coraline and Sandman series are a good place to start with Neil Gaiman, only if you are unfamiliar.
Good Omens is a collaborative work and unlike any other co-authored books (I am pointing to Patterson and Co.), it’s different and points out some good things about society and religion in general. Overall, this book is a piece of fantasy and show signs of humour from the start.
One, if highly familiar with both Gaiman’s and Pratchett’s style of writing might able to point out tiny bit of difference in the text but I think it is not much of a difference. The plot consists of angels and demons, good and evil and a tale of bonding between the two. The demon as we may call some of them, are not different and nor are the angels. In the start, a funny thing happens that develops the whole book and plot revolves around that part.