EDIT: after some digging, I found this article: http://www.theguardian.com/science/2012/jun/24/battle-of-the..., which summarizes the disagreement like so:
For lay spectators, the row is a symptom of the long and controversial
evolution of the very idea of evolution. At root it is a dispute about
whether natural selection, the theory of "the survival of the fittest" first
put forward by Charles Darwin in 1859, occurs only to preserve the single
gene. Wilson is an advocate of "multi-level selection theory", a development
of the idea of "kin selection", which holds that other biological, social and
even environmental priorities may be behind the process.
But Dawkins is far from convinced: "Wilson now rejects 'kin selection' and
replaces it with a revival of 'group selection' – the poorly defined and
incoherent view that evolution is driven by the differential survival of
whole groups of organisms."