The Unreal Tech page has been updated by Tim Sweeney, who talks about Direct3D anomalies that have been occuring during testing:

We've been looking at the feedback on Direct3D performance and investigating some strange reports. Recently, we've mainly been testing on 96-meg and 128-meg machines (I have a Celeron 400, Jack Porter has a K6-2 450). On these machines, TNT1 performance is good -- average 28 fps at 648x480, 25 fps at 800x600. The TNT2 performance is significantly better.

However, upon removing some RAM and testing Direct3D on a 64-meg K6-2, the "precache" time increased by about 5X, and performance dropped to a few frames per second. These performance drops don't occur in the software renderer, and don't occur in Glide. Something is going wrong between Unreal, Direct3D, and the TNT's Direct3D driver, and we're investigating.

Overall, the feedback indicates a very wide variance in performance among TNT users, much more so than with any other card. Our internal testing has indicated this too; for example, we've found (and worked around) a lot of driver bugs that only happen on one machine, and not others with otherwise similar configurations.

He later updated with some more problems,

Jack and I have been tracking down the performance problems with the TNT on 64-meg (and lower) machines.  To our great surprise, it appears that the TNT is keeping duplicate system memory copies of all our textures--we saw system memory grow and shrink in almost exact proportion to our "supposed" video memory texture allocations.  Thus the game uses an extra 12-26 megabytes of system memory--a very inefficient allocation of resources. This is a big surprise, because the NVidia guys has always told us this isn't the case.

Problem in my code?  I don't think so, but I'd love to be proven wrong.  I'll follow up with our henchmen at NVidia and Microsoft and see if we can track this down...

There is also a possible fix available for people with Monster Soundcards who are experiencing slowdowns when they enable 3D sound.