Never seen anything to substantiate that. Considering that dual 1GHz G4's tend to come up well short against a single P4 2 GHz, I'm not sure that can be substantiated. Yes, the initial P4 was slower than an equivalently clocked PIII - if you want G4 versus PIII, here you go.
Notice in your link that in various tests the slower G4 was faster than a higher-clocked PIII. The P4 is slower per-clock than a PIII. Complete the logic.
In your Digital Video test, the G4 was hampered by a new, unoptimized operating system. In those days the OS's GUI sucked up a lot of processing power, before it was later accelerated using Quartz Extreme. Speed improvements since then have OS X being much more efficient -- they make it faster every release (unlike another OS I know).
But none of this really matters for anything, and can only be guessing. I'd need this Apple machine, a Celeron and a Sempron all together to find out how the Apple stacks up against the competition.
And it really doesn't matter because in this market speed doesn't mean much. Small, cheap, quiet, low-power consumption and able to do basic jobs is what I'd look for.