I wouldn't recomend using a Pegasos or an AmigaONE as a web server if you plan to host anything more serious than a small web site. I wouldn't recomend using a desktop PC as a web server either. If you plan to use a dynamic site with a database behind it, then forget about it. They're just not up to the job. I have personal experience with how badly a desktop PC performs as a webserver, and I'm guessing the Pegasos and the A1 won't fare any better in this regard.
A decent web server should be able to support dual hot-swappable PSUs, hot-swappable PCI and hot-swappable HDs. That way you don't have to stop your server to replace parts that break.
It should also have SCSI RAID to be able to sustain the data transfer required, especially if you have a database. RAID is needed to use disk mirroring on two (or more) drives so that if one hard drive fails, the server will still be running.
Both the Pegasos and the A1 lack these features.
I don't know about the AtriciaS, but in standard desktop PCs the chipsets just can't handle the amount of data transfers that a decent server chipset do. I've seen a dual 600Mhz PIII server kick a 2.0GHz PIV desktop PC's behind in terms of speed when they were both used a webservers.
