Is there really any difference between OGLHA and D3DHA other than the obvious? I don't see any dramatic differences like I see with Software Rendering.
Well, the actual work is done by the graphics card, and that is the same if you use DirectX or OpenGL. So if the features required by the game and supported by the card are available through either API it doesn't make any visual difference.
There is a chance that the implementation of a feature is buggy in a driver, but the stuff required by FF8 should be so old and rock solid that you shouldn't have to worry.