Depends where it is... here in northern Alabama, rock would be pointless as it'd have weeds growing on/through it in a matter of months. Somewhere a lot drier rock would make sense, and if done well could/would actually look good.
So my personal opinion would be if it's somewhere that gets so little rain that the grass requires daily irrigation for it to grow at all I'd go with rock. If it's somewhere grass can grow and just needs to be cut I'd much prefer the greenery of the grass and vegetation. ...and if there's a shade canopy that prevents growth, I'd probably go with a mix just to keep dust down.