Avons, all the way.
I pretty much learned to ride on Dunlop K-81s so I really am fond of them. I have tens of thousands of miles on them; I know their characteristics. If I rode more on dirty roads, then I'd use them. On a dirt road, the Dunlops open (almost knobby like) side tread block pattern, similar to the K-70, is superior to the continuous pattern of the Avons. When you pick up the pace on a clean road, however, the edges of the K-81's open blocks get torn up and too little rubber is presented to the road. Then too, the transition from partial to full lean forces the tire to bridge the gap between the center tread area and the pentagonal outer edge blocks. That's why K-81s, especially new ones, signal a "slip and settle" to the rider when you make a quick turn in. Then, once you're mainly on those pentagonal blocks on the outside of the tire, the K-81 is nice and predictable, yet, in that moment it yields ultimate traction to tires that present continuous bands of rubber to the road. Sort of like a knobby vs a slick.
I wore out a set of 18" Roadriders on my 1986 GSXR 1100; loved them; I felt "ripped off" after I replaced them with some Michelin Pilot Power dual compound tires at twice the price. They were equivalent to the Roadriders on the street. I took both the Suzuki and the Commando out for a track day. The Michelins on the GSXR turned greasy in three laps. That same day, non-DOT roadrace Avons (not Roadriders) went onto my Commando - I could not overheat them. Admittedly not a fair comparison but I'm sold on Avons.