I wouldn't say that AMD is less stable than Intel. If you go all Intel, CPU, motherboard, etc then yes it would be. The stability of the system mainly comes from the motherboard and chipset. An AMD CPU on an ASUS motherboard with a VIA chipset is just as stable as an Intel CPU on an ASUS motherboard.
The main thing is if you want performance at any price go with Intel. If you want the best price/performance then go with AMD.
For Intel CPU's- for max stablility go with a Intel motherboard. For more features go with another motherboard manufacture like Asus or MSI.
I have a AMD Athlon XP running on an MSI motherboard with no problems, my computer hasn't crashed in over a month.