For a list of native software available for AmigaOS 4 see
IntuitionBase.
Are these platforms compatible? (I get the impression that they are going to diverge radically in the future, but that the current implementations are trying to achieve a large degree of compatibility with the Amiga OS 3.x API.)
They are only almost SOURCE code compatible to AmigaOS 3.9. There is an issue with the interfaces in the AmigaOS4 library system that makes the source code format different. They won't run each other's software without a recompile and MorphOS doesn't use all of the same APIs as AmigaOS. Keep in mind also that AOS 4 is not officially released yet and most of these comments are based on the developers' pre-release currently in circulation.