Half-Life was built with OpenGL, and therefore will always run best with it. In my opinion, you should always design your Half-Life mod using this mode. I suppose software mode may be better for some testing purposes, but that's besides the point.
Open GL doesnt like distance
That's actually not a problem with OpenGL at all, since you can set the view distance in the map properties. Maybe software mode can bypass this, but I wasn't aware of it, and in the end it gives you no advantage.
Direct3D, on the other hand, isn't so great with Half-Life. It wasn't intended to be used except as an alternative for people who had no other option. It won't display decals, and lighting will look much worse than when you use OpenGL.
Direct3D is the creation of Microsoft, and is considered very hard to program for. For these reasons, John Carmack, among other people, chose to adopt OpenGL instead, so all ID games use it. As you may know, Half-Life was based on the Quake engine, so it's obvious how OpenGL was adopted.
Microsoft was the only one (as far as I know) who ever claimed that their API was better for games than OpenGL, and they likely only did so to try and persuade developers to use Direct3D. What they said doesn't apply to Half-Life in any way, and OpenGL is certainly the most capable API to run it under.