I tried both and I am not noticing a difference in graphics or performance. Should I use one over the other or does it really not matter?

I'd like to clarify this unanswered topic.

Short answer: as the original author meanwhile probably has noticed: there's normally no noticeable difference.

The long answer is also valid for other programmes, not just this game.

OpenGL is the "industry standard" for accelerated graphics, while DIRECTX is specific to the Windows operating systems, and what most Windows applications use.

If you play on Linux:

You have no choice other than OpenGL, I didn't test if that is used silently nonetheless, if you set it to DIRECTX, or whether it fails to start in this case.

Exceptions:

You can (try to) play the Windows version on Wine; this WILL slow down everything, so should be avoided, except the native Linux version doesn't run (well) due to incompatibilities or bugs, or you're using a "helper application" for the Windows version (example: there's something to add an "automap" for an old game without one, I've forgotten the details). In these rare cases the Windows explanations below apply. The Wine approach should generally be avoided due to added complexity, as well as lower speed.

If you play on Windows:

Choose the one performing better:
1) If the game doesn't work or you experience bugs with one setting, choose the other.
2) If the game runs slower with one setting, choose the other.

Generally:

If you see no difference in gameplay, have a look at the performance: there might be a higher CPU/GPU usage if set to one of the two options, if so, you can save power by choosing the other.