The GeForce4 MX 440-8x has a core of 275 MHz vs. 250 MHz on the Radeon 9200 (non-pro); the 9200 Pro will generally yield higher performance. Most MX 440-8x cards also have the memory clocked slightly higher, at 513 (though it is NVIDIA's reference specs), giving a 0.5-1.5 fps boost in some games. Plus, the layout of texturing pipelines and mapping units is identical in both chips (2x2 for the GeForce4 MX and 4x1 for the Radeon 9200). It is that the higher core speed of the GeForce4 MX 440 8x gives it a theoretical fill rate advantage (and it could also apply to higher resolutions, where the performance is limited by fill rate), which can give it slightly higher performance at lower resolutions, but at 1024×768 and above, the Radeon 9200 can outperform it 99% of the time, due to a more efficient chip architecture (e.g. the crossbar memory controllers, where there are 4 present on the 9200 while only 2 on the MX).
Recommended drivers: (from personal experience)
GeForce FX cards - latest available
GeForce4 Ti cards - 41.09 (LOD Bias problem can be fixed with Riva Tuner)
GeForce3 cards - 30.82 or 31.xx
GeForce4 MX, GeForce2 and older - 29.42 or 30.82