By 'OpenGL' I assume you're referring to Quadro/FireGL as opposed to GeForce/Radeon?
Both nVidia and AMD make cards/drivers optimized for OpenGL performance specifically for high-end DCC (Digital Content Creation) and CAD use - applications such as Maya/3DS Max/AutoCAD etc. can take advantage of these optimizations for better performance.
But for general computing - games, internet, office apps etc. those cards have little-to-no benefit (and cost considerably more than their 'gaming' counterparts).
And as to how a card can support both OpenGL and DirectX, - they're just API's (Application Programming Interface) - a programmer writes to the API and the driver implementation (either nVidia's or AMD's) tells the graphics hardware what to do - either can be used since they're both supported in the drivers.
