I've had HL on several computers. The first computer, when I first got HL would run OpenGL, but it would be very buggy. That wasn't HL's fault or the computer's performance faults, it was a family computer and no one else knew not to go and click madly on the internet. Lots of spyware and bugs. It ate itself to death.
Anyway, I bought myself a spiffy new computer some years later and, because I'd screwed with the resolution settings and some other stuff but not the rendering modes, I didn't use OpenGL.
OpenGL looks far more like what is being presented in Hammer than software mode does. Also, because I will test maps on both modes, I know some maps don't work in software. They literally lock HL up. zeeba-g's 'Section 23', which is a beautiful map in OpenGL, has very low framerates in software mode.
Kasberg's 'Tokyo Museum' map would load, show up, then when the player moves, HL promptly closes.
The only complaint I have with OpenGL is that when I window switch out of HL, the resolution doesn't change and I get a zoomed in desktop.
The only things I can say about Direct3D is that it takes a long time to load and doesn't look much different than OpenGL.