If he believed his version was superior, why suppress Brownlow's and not let it compete with his?
This just doesn't really resemble the film's history that much. This is my memory of how this has played over the years, if I'm wrong on any details, please correct me:
The reconstruction
is Brownlow's. Napoleon is a film with no definitive shape and it is not necessarily better with every last scrap of film in it. Hold those thoughts.
After the Telluride film festival honoring Gance (Telluride being run by, among others, Coppola pal/adviser Tom Luddy), Coppola was involved in acquiring the rights for US screenings, which would never have happened on such a scale without his backing. He did so, it seems clear, in large part to give his dad a showcase as composer and conductor.
Union rules in the US made a screening over 4 hours prohibitively expensive for live orchestra. So Brownlow created a US cut which runs about 4 hours, and that's what Carmine Coppola scored. Insofar as ANY cut of Napoleon constitutes Kevin Brownlow's choices about what makes a coherent version of the material, one should not mistake this for being like Miramax cutting a half hour out of a contemporary director's finished work— but rather a practical decision by Brownlow to construct a workable version of the movie at a certain length. (It's possible someone else cut it to 4 hours, but Brownlow at minimum accepted this as a necessity for the symphonic tour.) Up to this point, I think everyone was happy and friendly.
Years pass. Carmine Coppola passes away in 1991. And Brownlow continues to find pieces, so Napoleon grows and grows. At some point the version released and occasionally screened in the UK and elsewhere is notably longer than the Coppola-US version. Brownlow wants to release a longer version in the US; Coppola wants to preserve the version his dad worked on. I disagree with that, or think there could have been a way to fudge a longer version with music by his dad or by someone else in a similar style... but again, we're talking about two competing Brownlow-shaped versions.
And in the end, Coppola has agreed to a screening of this latest version with music not by his dad. What a terrible guy!