While native apps give the most freedom in terms of functionality (you can do anything you want, within reason), there is a much larger cost and time overhead if you're creating the book from scratch (e.g. coding how page transitions work, how content behaves on each page, etc). The visual design is also more flexible, but unless you've built special tools for them your designer will need to find their way around XCode (Apple's development environment) which can be a steep and frustrating learning curve.
iBooks Author, on the other hand, does a brilliant job of simplifying the design and production stages – all of the hard work in building an infrastructure for how pages and content behave is done for you. This simplification does mean that design choices are sometimes limited and can constrain the visual outcome of a project. You can spend a lot of time trying to find ways to work around a particular unexpected restriction.