It's true that GA claims to offer demographic reporting. The reliability and usefulness of that reporting is a different matter, of course.

Other than that, Piwik might be less capable if you just install a standard baseline and never customize it, but when integrated with a little custom logic it can do some pretty impressive (and, in particular, tailored) analysis and visualization. GA is more the other way around. You have more tools available as standard, but then it has limited scope for useful customisation beyond its built-in toolset (edit: without resorting to building completely bespoke systems via APIs, that is).

For example, I've seen quite simple situations that seem enough to confuse GA's funnel tools. A common one is a non-linear sign-up funnel where some steps may be skipped or changed, or where a visitor may come in part-way through the process. These often happen in practice because of something that visitor has already done before starting to sign up, where they are located, how they choose to pay, or other factors. My experience has been that anything remotely unusual like that immediately seems to confuse GA's entire funnel toolset, rendering it all but useless. With a more flexible tool like Piwik you can generate a custom visualization of the whole process you actually use with a reasonable amount of effort.