I think Laughing Gnome has a great system. I think two different hops per one fence wall is something you could control, and continue to tell apart and redirect them whereever you want. I can imagine having three or four different plants and mid season having no idea where one hop begins and the other ends. Two seems identifiable. I'm thinking, "The left one and the right one."
I could see the ambitious horizontal hop grower having different types on different fences. If your yard has four sides, thats eight possible different hops... if your ambitious.
I have four growing vertically and this year I've considered planting more in my backyard. I may go horizontal. I'm definitely pushing the limits of 'friendly neighbor". I think horizontal is less obtrusive and that may keep my property looking normal rather than like the suburban hop farm it's turning into.
Growing hops is like making beer. We all have opinions, but it comes down to whats best for you. Horizontal growers need to build a strong trellis, which can be hard to make and an eye sore, but hops like "up" and after they start there is little work involved.
Vertically any fence/structure will do. Effort is low in trellis construction and its not unsightly, but you need to pay more attention to your hops to make them stay on the vertical structure. This isn't a bad thing, I bet the vertical grower spot hop issues faster than the horizontal. There's a case for vertical growing.
Just protect your dogs and remember when the year is done you need to harvest your hops and pull those dead bines off your fence. A string is easier to "de-bine" than say... lattice. Whatever your system, think about sun, water, drainage, ability to harvest, and "de-bining". I started two hills with local large rhizomes, and two hills with two small mail order rhizomes. The strength of the bines seemed more dependant on how much they were attacked by Japanese beetles than by the size of the starting rhizome.