I tested both single and dual core Intel minis a couple of weeks ago, and they both outperformed my Dual 867, and the dual core model got very close to the performance of my Rev A G5 dual 2.0 running iMovie 6.
In terms of performance in native software, I'd expect both Intel minis to outperform a dual 1.25 G4 on almost all tasks - the only exception might be between the G4 and single core mini in tasks which are highly processor intensive, where the dual G4s might still win out, or on disc-intensive work (meaning opening or saving something like very large photoshop files rather than streaming DV in iMovie) where the mini's drive speed would still represent a bit of a possible bottleneck.
I was quite impressed by the Intel units, particularly in iMovie where my G4 minis tend to be a bit laggy as projects grow, but even the single core mini was much more responsive.