There is no problem at all using AMD athlon or Duron with emus. The eventual problems are not processor related, but mostly chipset ( VIA doesn't make the most reliable chipsets ) related.
I have a Duron 800 CPU, a Epox 8KTA2 mobo with the VIA KT133 chipset.
There is a bug in the VIA southbridge chip and for months VIA ignored the problem ( UDMA not worhing on the 2nd IDE interface ) but now my system is as stable as a rock after installing the new version of VIA 4in1 drivers and flashing the nobo BIOS to the latest revision.
Now, maybe VIA improved its reliability with the recent DDRAM chipset but other companies are issuing chipset for the Athlon CPU: Nvidia SIS AMD among others.
Please be sure to have a RELIABLE high quality high output ( 300 watts ) power supply ( Antec for instance )
And Adair is right, with such an upgrade, EPSXE will really fly, maybe you'll be obliged to LIMIT the framerate ( the emu will run too fast ) if of course the bottleneck is not shifted to your graphic card ( you must match the graphic board to the processor ) or it's like having a big powerful engine connected to a weak and fragile transmission .
So, all in all AMD Duron or athlons are the best bang for the buck right now when buying a processor.
I hope this helps