Trio64 is the newer one, and uses conventional RAM (FPM) compared to the VRAM the predecessor, the Vision series used.
The Trio64 enjoys very good DOS compatibility throughout the board, and is clocked slightly higher than the Vision968.

Both will work for your purposes, albeit the Trio64 is a sure bet to suit you well for your DOS and GUI needs.
Be sure to use the S3 utilities to squeeze the most performance out of the Trio64.

Trio64 belongs to the consumer lineup and Vision968 to the professional lineup. Technically the Trio64 integrates GPU + DAC + clock generator in a single chip.

The Trio64 has a 135? MHz DAC integrated and the Vision968 DACs vary usually between 170 MHz (with 2 MB VRAM), 220 MHz (4 MB VRAM) to 250 MHz (8 MB VRAM). More RAM allows higher resolutions, thus a higher clocked DAC allows high refresh rates at these high resolutions.
As example look at that Diamond advertising: http://retronn.de/imports/diamond_bible.html
The Stealth 64 Video can still do 90 Hz at 1280x1024 True Color, while the Stealth 64 DRAM goes up to 75 Hz at 1280x1024 at 256 colors. Also note that for the Stealth 64 DRAM the Vision 864 and Trio64 is listed as variants in the same line.

Feature wise the Trio64 matches the Vision 964. The Vision 968 support video overlays and YUV to RGB color conversion with linear interpolation. So the Vision 968 matches the Trio64V+.

For DOS:
Trio64 is mostly slightly faster than a Vision card. Not much other difference.

For Windows:
Vision based cards can have more Video RAM and thus run higher resolutions/color depths. With TFTs the high refresh rates are not so important, though the higher clocked DACs give generally a sharper image. Due to the VRAM the Vision is faster with accelerated functions such as BitBlt in higher modes as the Trio64 suffers a bit from bandwidth limitations of the DRAM. Though this happens only at high resolution/high color depth/ high refresh rate modes. As most games use like 640x480 at 256 colors it is not an issue for games. For Win9x generally the S3 driver that comes with DirectX5 is fast and reliable.

Is univbe important for a Trio64, or is the built-in VBE2 support already good? And did S3 have their own Trio VBE driver for DOS? (I'm only finding Windows drivers, nothing for DOS.)

I usually use S3VBE: ftp://retronn.de/driver/S3/VESA/

Indeed I was mistaken when it came to the clock speeds. My Trio64V+ clocks in at 135Mhz and the Trio64V2/DX at 175Mhz respectively. But their performance doesn't differ that greatly. Could this be due to the new features added?