Well, I don't think, it's astonishing, that things aren't working properly, if no real OpenGL driver is being used. Are you really sure, that there's no better driver for your VIA card on Linux?
Well, I thought that I had the best driver selected, but apparently my machine was using the generic vesa driver. I tried to change it to the VIA driver, but this screwed up my xserver and I had to go into my xorg.conf file and add in a bunch of stuff and I was never able to get it to work. I found an openchrome driver that supports my graphics card, but the version was 0.2.xxx so I was a little skeptical and when I tried to run the Q3Benchmark I got a really weird error (I will post in a little bit I am on my Windows machine right now). By the way, I am pretty new with Linux so I could be screwing something up I don't see what I could be messing up though.
What about the DisplayLists using tests like e.g. the Q3FlightBenchmark for your second system with the ATI card on Windows? Does this work?
On my windows machine I am not able to get the Q3FlightBenchmark to work I get the dark gray screen and the past three or so times that I have tried to run it I eventually get a JVM error the file with the error that Eclipse automatically created is attached.
PS: Thanks for the feedback, btw.
No problem, I'm glad to help in any way that I can. And btw, good luck with your exam.
EDIT:
Here is the error that I get in the console on my Linux machine with the openchrome driver.
Initializing JOODE...ok
0000: f0000001 00000300 f0000006 00000000
0010: f000000b 00000000 f000000c 002802a0
0020: f000000d 002802a0 f000000e 81940194
0030: f0000002 00000000 f0000003 00000000
0040: f0000004 0257031f f0000000 f0002001
0050: f000000b 00000000 f210f110 00010000
0060: cccccccc cccccccc cccccccc cccccccc
0070: cccccccc cccccccc cccccccc cccccccc
******************************************
fire_buffer: DRM_VIA_PCICMD returned -22
Sorry if this of much use, I am trying to find another driver so hopefully I can post some actually useful information

. But, regardless, I should have my new video card come Monday or Tuesday (fingers crossed) so at least I will be able to start working with Xith again.