People frequently ask why a project would want to move to Apache. The most recent case of this I have run across was in a thread on CouchDB's graduation, on Reddit. To answer the question, I'll take my apache hat off for a moment and put by consumer internet company architect (who codes as much as I can make the time for!) hat on.
The biggest benefit, to me, is that Apache provides a known way of doing things. We (remember, I have my $company_man hat on) don't use Couch right now (though we have certainly talked about it), but a major factor if we choose to use it is how the code gets developed, and how we can influence that in the direction that we need. With Apache, we know how it gets developed (in the open, all decisions on public mailing lists) and how to get involved (submit bugs and patches which will be discussed on the mailing list, if we need more keep submitting patches until they get tired of applying them and make me a committer, as committer keep working in the open, etc).
If you need to have influence over the project, say because you are creating a strategic dependency on it, you absolutely know that you can gain as much influence over an apache project as your competence allows. This is crucial, as the alternative is the willingness to maintain a fork if the developers go berserk, wander away, which happens. A major part of technology selection is balancing risks. It is not being totally risk averse, but it is being aware of the risks in critical dependencies and making the choice to accept the price if that risk converts into a liability. Having a guaranteed way to provide continuity to a project in the face of typical project killers, such as the project leader leaving the project, trumps merely having freedom to fork.