As long as you have a powerful enough power supply and in some cases RAM is kinda picky then AMD can be quite stable.
I'm running an old Asus K7M AMD751/Via686A board and it has excellent stability. I think in the PC platform stability comes much more from what OS you use than what platform. As long as you use high quality components for any combination.
An Intel platform has excellent stability, but so does a properly set up AMD platform. I'd worry much more about what OS you're running than what hardware. Hell if you know what you're doing you can get Win98SE running just fine. There are still memory leaks and you can't run 24/7 for ever or you'll have no RAM left, but my Win98SE machine hasn't crashed in months and months...
Just get a good mobo (Asus, Gigabyte or Tyan are my personal favourites and in the case of the KT133 MSi is also excellent), good RAM, and a good PSU and your system will be fine.
However you might want to consider Intel CPUs with ServerWorks chipsets....(like the Asus CUR-DLS) the ServerWorks chipsets are supposedly exteremely reliable...they also offer alot of RAM and on onboard SCSI/LAN
Oh yes...I would just like to interject at this point, that neither AMD or Intel systems are really terribly stable. If you stability try a Tandem system or even an AS/400, there are pretty small 400s available

VMS systems are pretty solid to...anything from Sun (and man those new SunBlade are damn fscking sexy....) hehehe but you just asked for a comparision of Intel/AMD and I think they are pretty even.
