I hunt both ways; with dogs and with calls. My in-laws have coyote hounds and they do a fantastic job. Without question the houndsmen have the upper hand.
It's the hunters choice on method of hunting and what fits their needs for their geography and budget. I grew up near Mosquito Creek and land availability is abundant to let hounds run. I now live in Eastern Pa, where calling is a little more conducive to the area due to lack of land available. Plus hounds running with all the big interstates is recipe for disaster.
So here is my opinion: without question the houndsmen have the upper hand. I did it, I experienced it, and I enjoy it due to the fast pace and pleasure of hearing hounds on a fresh track. Plus the success rate is fairly good. As long as you have a small group of guys your chances of getting in the right spot to take the shot at the coyote is good. Not saying it is easy, but with knowledge of the land, men with multiple trucks to navigate from one side of the mountain to the other, as well as GPS units on the dogs, chances exponentially go up for a kill compared to calling. I compare it to a Pa bear drive; 25 guys pushing a bottom out and the bear eventually shows up in front of someone. But it's the hunters decision on how he or she chooses to pursue coyotes. I am now primarily a caller, with a periodic weekend with the dogs. Calling coyotes is, in my opinion, more technique and ability driven; you have many aspects to consider including wind, sound choice, volume, setup, etc.
In summary, both are fun methods of hunting and rewarding for many different reasons. BUT, I do think it should be two separate classes to enter at the annual Mosquito Creek hunt. 1 division for the houndsmen and 1 division for calling. It would delineate the two methods and equal the playing field. The way it is now the average hunter (the majority) with an ecall or hand call is competing against a group of folks who have invested thousands of dollars and hundreds of hours to the sport while capitalizing off the average hunters entry fees with the majority of the wins (historically over the years this is the case). It's similar to building a race car in your garage with some side money and competing at the Daytona 500 nascar race against the big race teams.
Again, both are great, fun methods of hunting coyotes but shouldn't be lumped into one division competing for the purse at the Mosquito Creek hunt.