1) Stability. I have had MorphOS 2.4 lose the keyboard on a G4 Mac Mini. I'd have to unplug and replug. Both systems have had odd freezes. Any other stability issues on either side?
MorphOS is by far more stable than Aros. I never had this Keyboard problem on my Mac Mini G4. Are you using a USB hub? Otherwise, you might want to try a different keyboard.
2) Amiga emulation. I've been told you can launch a classic Amiga app on MorphOS as long as it doesn't bang the custom chipsets. Can AROS do this? How does MOS do it? For games that do bang the hardware, is UAE required?
Yes, UAE is required for classic games on both platforms. For WB friendly apps, MorphOS uses Trance, while Aros has a different approach (firing up a minimal UAE in a transparent way).
3) How easy would it be to build something like pidgin under AROS or MorphOS? Do they support the standard GNU tools?
Porting such applications will be more or less equally difficult on both platforms. Of course, there's GCC for both of them.
From an end user POV, MorphOS clearly is the better choice at the moment. Better stability, very advanced version of OWB, good compatibility with classic applications etc. etc. But it is fairly expensive + your license is locked to one machine. However, if you are into tinkering, I suggest you give Aros a shot. Part of the fun is that everyone can contribute, it works on a large variety of hardware (including laptops), and it is free. I think in the long run, an open source Amiga system will be the only way to go.