MorphOS is a very nice system, Ambient the user interface gets updated almost daily and is making great progress. If you don't like Ambient there's also Scalos wich is pretty good and very Amiga like.
Shogo, Heretic II, Wipeout, Quake 2 and Freespace run very well, no problems on my system. There are also other games like Quake III, Hexen II and Virtual Grand Prix available.
E-UAE runs most demo's and games fullspeed on a Pegasos, the speed of E-UAE is about 50% of a stock Amiga 4000. The waiting is for JIT to make the most of it.
Most Amiga programs run on MorphOS as long as they don't make use of the custom chips of the Amiga. I'm running TVPaint, Directory Opus and a lot of other Amiga programs on my Pegasos.
And yes it's true there's not a modern browser or office packet available for it but that aplies to all Amiga's including A-One and OS4. But there's hope, KHTML is just around the corner

It's even possible to run OS4 programs on MorphOS but I have not tried that because IMHO there's no need to run OS4 software on MorphOS.
The Pegasos II board itself is pretty nice and supported by various Linux distro's, I'm running Ubuntu Dapper Drake myself.