Okay, let's get some things straight
1) All 3dfx-based cards (Voodoo Graphics, Voodoo Rush, Voodoo², Voodoo Banshee, Voodoo³, Voodoo 4/5 [VSA-100]) support D3D, OpenGL, and Glide. That includes cards made by 3rd party manufacturers (Creative, Diamond, etc.)
2) All 3dfx-based cards (see list above!) can use the standard 3dfx reference drivers. The 3dfx reference drivers may not have all the extras of the 3rd party drivers, but they are normally less buggy (the drivers from Diamond certainly come to mind when I think of bugs!!!).
3) All combined 2D/3D 3dfx-based graphics cards (i.e. all except Voodoo Graphics and Voodoo² cards) support 32bit colour in 2D resolutions. This includes desktop colour depth.
4) 2D-only 3dfx-based graphics cards (Voodoo Graphics and Voodoo² cards) only support 16bit resolutions.
5) Only the Voodoo 4/5 cards (using the VSA-100 chipset) support 32bit colour rendering and 32bit colour textures in 3D modes of D3D, OpenGL, and Glide.
So, to address the problem/comments :-
cooliscool: Your Voodoo³ card can not support ARGB8888 (32bit) rendering, so it will not work. No wonder you get crappy graphics
Stick to 16bit rendering modes (ARGB0565, for a Voodoo card).
rio: yup, correct answer
Biased turkey: what you say is true, although I always say that you should use the plugin that works best for you. I know my plugin doesn't work better than Pete's with certain games, and on certain people's systems (Pete and I tackle certain emulation problems in different ways), so you should always do your own comparison.
Kna127: The Diamond Monster 16Mb is a Voodoo Banshee card. It is no different than any other Voodoo Banshee card out there, afaik. I hope you aren't using the Diamond drivers!!!! But yes, you can use Voodoo³ drivers with the Voodoo Banshee, with a bit of hacking. I couldn't say whether this is a "Good Thing" (tm) to do, as I've never tried it myself. Although I am slightly confused about you "turning off the banshee chipset" option! The only one I can think of is in my plugin. Is that the one?
sxamiga: whoa, lay off the happy-pipe
You don't have to disable anything for a 3dfx-based card to work in D3D or OpenGL. You just run the program, and it works. So a Voodoo Banshee and Voodoo ³ card with work fine with both my plugin and all of Pete's, as long as you select 16bit rendering modes in Pete's plugin (as noted in his readme).
dpence: Biased turkey made sense to me, it was the next couple that didn't make sense!!
Apart from that, what you say is true, although [again] check all plugins for yourself and find which works best for your setup with your games .... my usual disclaimer
fivefeet8: 8888 does help, even with PSX games. It helps reduce the colour banding that gouraud-shading on the PSX can produce. On the PSX, they can selective enable dithering, but it doesn't beat higher colour depths. Also, with 8888, 24bit MDECs can be reproduced with no colour-loss, whereas in 1555/0565 modes some of the colour information is lost when the MDECs colours are reduced to 16bit.
Note: my plugin automatically uses 8888 rendering and 8888 textures on Voodoo cards that can support it (i.e. Voodoo4/5 [VSA-100]).