Exactly! An effective fly is an effective fly, period. I just like to tie and fish with nice, well-tied flies.
An example of differing effectiveness was what happened yesterday in the late afternoon/early evening on the Skagit. Ed Ward, big John form Chicago, and I fished through the same run together. Each of us used very different flies that had a different swim profile in the water and which swam at different water depth relative to the sink tips we were using. All of us were presenting our chosen flies with a classic across stream wet fly swing. However, only one of us had any action, and he missed two fish and landed a very bright hen that still had sea lice on it.
The only real difference between the three of us was the type of fly being used. And on that particular day, with that particular river flow and water temp, only one of the fly types was effective. And all three of us were using what many call fancy flies. Ed was using one of his Intruders, Big John was using a Marabou Spider, and I was using an Ally's Shrimp. On a different day, one of the other fly types may have been the most effective.
Is this always the case? Of course not! There are days when several different fly types will garner takes, and others where a specific fly type or color will illicit takes.