It's really hard to tell on this one without seeing the guts of the Duron system. A homemade system is only as good as its builder. You could find a great ASUS board in there, or you could find a PCChips piece of crap. You could find that someone was picky about the optical drives, or that they bought whatever some computer-show vendor was hawking cheaply at the time. Same goes for all the other parts, and that's not including the care they took when building the system. Did they do a good job of cable routing? Choose a good case/power supply? A well-made homebuild Duron 850 would likely outrank the P3-933. A poorly one would fall below it.
Check if the HP will allow an AGP graphics card as an upgrade. If it will, it may be the better setup. If not, then it really depends on how the Duron system was put together.
P.S. While the Duron may be overclockable (probably easily so, if you know what you're doing) I recommend against overlcocking a system that goes to family and friends. Once it's out of your direct supervision, a system that's being pushed beyond specs can be asking for trouble.
Intel Q9450 @3.2GHz, Gigabyte GA EP45-UD3P, 4 x 2GB G.Skill @4-4-4-12
Antec P160SW case (modded), Xigmatek 750w PSU
3x 500GB (RAID-5), , OptiArc 7200S, ASUS E818A3T
Creative X-Fi XtremeGamer, Hauppauge HVR-1800, Radeon 4890