These are cards from very different times, although only 3 years have passed.
They focus on different directX.
The 9600XT sometimes outperformed the FX5950 in DX9 tests and was a direct competitor to the 5700 (ultra).

For Windows 9x and dx7-8, GF 2-3-4 and Radeon 7500/8500/9200 look more organic.

I agree with shevalier, I'd also go with GF2 GTS, it's a perfect match for PIII 1000, period correct, also a high end card.

9600XT would be more suitable for a mid range computer with Windows XP, paired maybe with an Athlon XP.

PIII 1000 + 9600XT is a weird choice.

GeForce 2 GTS:

Pros:
- Table fog and paletted textures support (good for old D3D games)
- Less driver overhead with early drivers
- OMG it's Nvidia, you absolutely can't go wrong with GeForce!

Cons:
- Crappy 16-bit dithering
- Performance is dramatically worse with 32-bit color, not suitable for high resolution modes
- S3TC texture bug
- Image quality is worse
- Can't properly emulate all 3dfx Glide features (no shaders)

Radeon 9600XT

Pros:
- Decent 16-bit dithering
- Superior image quality
- Mostly accurate and feature complete 3dfx Glide emulation with Shader Model 2.0 support
- Much faster for high resolution modes, especially with 32-bit color
- TruForm feature support with early drivers

Cons:
- Driver overhead
- Only table fog is supported, with not paletted textures, so overall less compatible with early Direct3D games
- Not compatible with Intel 440BX chipset

The Serpent Rider wrote on 2023-09-20, 08:53:

Only table fog is supported, with not paletted textures, so overall less compatible with early Direct3D games

To clarify this, table fog is only fully supported on Radeon cards under WinXP, when using Catalyst 7.11 drivers or newer. Under Win9x, you can enable unofficial table fog support via registry tweaks. However, the fog will not look the same as on Nvidia/3DFX/Matrox cards, and it still won't work with certain games (e.g. Shadows of the Empire).

On the plus side, the 9600XT supports EMBM while the GeForce 2 doesn't. Image quality (sharpness) is much better on Radeon cards as well. Lastly, the 9600XT allows you to crank up Anisotropic Filtering to 16x, with minimal impact on the frame rate in most games.

By image quality, I meant horrible blocky texture filtering, which plagues all Nvidia cards of that period. GeForce 2 GTS had options with DVI ports.

Now for DOS, Nvidia card is much more straightforward choice, because it has VBE 3.0 support.

Thanks all! Very useful information. Will go with the NVIDIA GeForce 2 GTS for now.