Living with MOS/AOS4/AROS only

[Fab]

And how good is the best browser available?
http://en.wikipedia.org/wiki/Origyn_Web_Browser

Depends on the port. The 3 versions of OWB for MorphOS, AROS and OS4 are all very different in features or stability.

It is based on webkit. Why it's not as good as safari or chrome?
Why it can't render google documents or gmail?

Who said it couldn't work with google docs or google mail? It can.

[Fab]

Oh, and Google documents seems slower than OSX tiger (same HW, of course)

Google document is a bit slowish, but let's not forget everything is rendered with software cairo there.
On the other hand, video playback is way faster than OSX on the same hardware, be it with mplayer or with owb html5 video (when it's in overlay mode).