Rival Schools definitely works in Mame. You (anyone who doesn't already know) should get Mame32 Plus! Plus! 0.114. It has support for games like Rival Schools, Battle Arena Toshinden, etc.
You can configure PSX plugins and stuff to help make them games run a LOT faster. I tried to run Rival Schools in Mame32 Plus! Plus! using just the emulator and not the PSX plugins... I couldn't get anywhere near 40 fps.
Then I tested it with PSX plugins and it doubled the uncapped frames during gameplay in Rival Schools.
Rival Schools USA
You can also limit your maximum frame rate. I use this exact configuration for all 3D games.
Create a folder called plugins in your Mame directory and put these plugins in it.
Graphics plugin: d3d_renderer (obtain renderer.znc from OpenGL and D3D renderers 1.2.zip, on this site where you get Zinc from, and rename it to d3d_renderer, it cannot be configured)
Sound plugin: spuPeopsSound.dll (Can be configured, download PCSX2 0.9.2 from this site and take spu2PeopsSound.dll from the plugins folder and rename it to spuPeopsSound.dll).
Set your controls before you launch any 3D game using the PSX plugins.
Go to Advanced > change video out method to 3D, start the game, pause it, set your controls, exit, then restart using the PSX / GPU (3D Graphics plugins).
Battle Arena Toshinden 2 USA
Street Fighter EX 2 Plus USA
Strider 2 ASIA
Bloody Roar 2 JAPAN
Tekken 3 USA