What's all this for "Overlay" and "DDraw" and "OpenGL"? Being that Duke3D's sprites are all flat, would fiddling with this make any difference?

Yes, I agree with Ralackk. See, you aren't running Duke in DOS, you are running it in DOSBox which itself runs in your Windows OS. Therefore DOSBox needs to use graphics drivers to output the display within the Windows environment, and it does so using whichever option you choose, be that DirectX, OpenGL, or whatever else.
There are some posts on these forums where some of the modes don't work for some people but others do, so it's probably hardware related.
You could always use eDuke32 or similar which is a different engine for the game and allows true 3D models.

so, is it like switching to a SuperEagle filter in a console emulator?

Whats the SuperEagle filter do?

It's just a filter that console emulators like Gens or ZSNES use. It kinda blurs the corners between and around pixels, giving them a "rounded" appearance, and thus giving sprites and backgrounds a "higher def than before, at least" appearance.

Well in that case I think some of them sort of work like that. I believe opengl uses bilinear filtering that blurs the image a bit. Surface is normally most compatible but doesn't allow scaling, where as overlay will alow the image to scale.
I still don't think you will notice much off a difference if any between the options, just use whatever works or gives the best frame rates.

No, for the SuperEagle-style effects you need to play around with the "scaler" option in dosbox conf file. advmame3x, hq2x, etc. The hq filters look best, but they eat CPU cycles for breakfast. Best bet would be to download gulikoza's build and use either the openglhq output or direct3d output with an hq pixelshader. That way the work will be offloaded on your video card instead of taxing the CPU through software.

hq filtering looks best on pure 2D games though. here's an example i posted for Master of Magic

But... it looks so bad!

I'm an "openglnb" guy. Exactly like what the original game looks like.

I hate those aggressive filters. Makes the game look like a color photo somebody slobbered on.

To each his own. In some games I set fullresolution to something lower, like 800x600, and let my monitor or drivers scale it up to monitor native to add a softer touch to the hq filter.

You might try the HRM option that's linked here: http://hrp.duke4.net/index.php Doesn't really answer you're question, but it pretty much blew my mind when I started playing it.

It does include some hackery to make it work, but it's pretty amazing work.