The biggest advantages I see, with the continuous-surface hones (Dia-Sharp) are:
1.) More uniform finish left by the continuous-surface hones; especially noticeable at the finer grits.
2.) No 'holes' (or 'dots') to inadvertently snag a tip on the continuous hones; sometimes the belly of a blade can also snag a little bit in the 'dots' on the Duo-Sharps & Dia-Folds, if pressure is just a little heavy, or if the angle is a little too steep.
The 'Duo-Sharp' hones (interrupted surface) are manufactured to precision flatness, which is nice for sharpening tools with dead-straight edges, like chisels and plane blades, and also for lapping oilstones & waterstones. For the typically-curved edges of most cutlery, this is essentially a moot point, as the edge only contacts a very small area of the hone at any given instant. The Dia-Sharps are quite flat, just not to the same tight tolerances as the Duo-Sharps.
In terms of speed of metal removal, they're both quite fast in the larger bench-sized hones, and the continuous hones have the speed advantage in smaller hones, especially pocket-sized versions (I prefer my 'credit card' hones over my Dia-Folds for this reason). Use a little bit of water, or water + dish soap, or mineral oil to keep swarf from clogging the surface, and either type will perform very well.