Wider stones make it easier to evenly grind & shape an edge without creating gouged or rutted areas along the edge, for a couple of reasons:
(1) I used to use a Lansky guided system with 1/2" wide hones. Their narrow width meant I needed to be more careful to avoid overgrinding a small portion of the edge, as the narrow hones make such errors a lot more visible and ugly. That alone is a good reason why you always want to go with a wider stone, versus a narrower one.
(2) Additionally, wider hones will be less prone to tipping and rocking from side-to-side as you sharpen. In simple terms, the wider stones have a more stable base of contact. That rocking instability of a narrower hone will cause the edges/corners of the hone to gouge your blade's edge bevels - and that's really ugly when it happens. This was another thing I noticed in using those narrow Lansky hones - they were much more prone to tipping to the corners.
There'll also be some small advantage due to the larger surface area of a wider hone, assuming length is the same. The point of contact between knife edge and the hone will move across the larger diagonal (corner-to-corner) dimension of the wider hone, meaning you're getting a little more abrasive contact on each pass. The difference in this is more obvious when going to something much larger, like a large bench stone at 8" x 2" or larger, where you'll see a dramatic increase in grinding speed to get the job done.
