@iamaboringperson,
TO begin with, I am behind the MorphOS camp, so this is as I see things. This also means I do not see a grander picture for AOS4, using only the demonstrated segments and the whitepapers to judge from. So, let's start from the bottom:
The problem is that the AmigaOS API's, while nice, are also unstable: a single errant program can kill the whole setup.
MorphOS is based on the premice of keeping these legacy API's safely away from the core of the system, in order to prevent it from taking down the whole system. With MorphOS putting these API's into a lock-box, if an errant program does go awry, the system can kill the whole box off and keep the rest of the programs running smoothly. This works in much the same manner as WinOS/2 or Mac OSX's classic compatability mode.
AmigaOS4, by comparison, is trying to have it's cake and eat it too, by integrating new, safe, API's alongside the older, unsafe, API's. I am not assured that this approach will work, as shown by the repeated failed attempts to do the same thing with MacOS before they abandoned the concept and went with the same approach as MorphOS.
That's just from the basic principle on how they work, mind you.
As for more concrete:
MorphOS's GUI, Ambient, is built directly on top of CyberGFX and is built up using MUI.
AmigaOS's GUI, Workbench, is still based on Intuition and the legacy widgets for core operations.
MorphOS, by building a full version of MUI into the system, provides a consistant level of programmability from the top to the bottom.
AmigaOS, by comparison, not only includes the legacy workbench material, but also includes ReAction and a shareware form of MUI, which means it has more availible applications but no guarantee of consistant operation between them.
MorphOS runs on both legacy PPC cards for the Amiga and a next generation PPC platform, the Pegasos. The Pegasos version is more advanced, but the ones for the classic Amiga still are under development and have a public beta availible.
AmigaOS 4 at this time, only runs on the Cyberstorm PPC. Plans for the AmigaONE and BlizzardPPC are forthcoming, but nothing is in a demonstratable form at this time.
MorphOS utilizes a hardware abstraction layer in order to help get rid of the legacy hardware dependence when not on the Amiga hardware. This is called Open Firmware, and is an industrial standard HAL found in mainframes, workstations, and even your local iMac.
AmigaOS's plans for moving off of the classic Amiga hardware involve using a Linux boot-strapping BIOS called uBoot, which was engineered for embedded motherboards (like those found in your microwave or DVD player). AmigaOS4's main authors helped to port this to the AmigaONE.
MorphOS includes registered versions of software such as a web browser, e-mail, MUI, etc.
AmigaOS4 includes much shareware, including the widget set MUI needed for it's shareware browser, IBrowse.
That's all I can think of off the top of my head. Feel free to flame and nit-pick this appart. But remember, this is from my personal POV, and do recall that I am biased to the OS that I can use today.