I think those who have used wood-fired offset smokers have become accustomed to the smoky taste.
Cured wood has a much higher moisture content than pellets and the pieces of wood are much different in size and shape. Thus, wood burns differently than pellets. I have read some speculation that the variation in cooking temperatures as you tend a manual feed firebox might also contribute to the flavor.
I have never owned an offset smoker. Sometimes the smoky flavor of Traeger is too much for my wife and I, but I can understand that coming from an offset smoker experience is quite different.
You might be interested in this thread about adding a Smoke Daddy generator to your grill. That might be the only way to replicate the offset smoker experience on a Traeger.
Full disclosure: This will be a pretty comprehensive review that will be updated over the coming year as I gain more experience using it. I bought the Smoke Daddy Magnum PIG to modify my Traeger Pro 780, which is a fantastic pellet grill and highly recommended - that offers little to no smoke...
www.traegerforum.com