Based on my limited experience, plus what I've learned from others, I'd say it's not brand, but construction...and it's not the effect on taste, but performance.
The couple of higher end pipes I have are definitely superior in construction and performance than most of my lower to mid range pipes. BUT, I do have a few low to mid range pipes that do smoke just as well, or almost as well.
I think the difference is consistency. For example, if I were to acquire another Ashton or another Baki meer, I realize that there is no guarantee that it will turn out to be as good as the ones I have...but I believe the odds of that are very good. Whereas I have a couple of Savinellis that are wonderful smokers, but I also have a few that are mediocre. If I buy another, it may turn out to be great...but my perception is that it is more of a hit & miss prospect than the higher end or custom pipes.
I think the best route is to purchase as much quality as possible, while avoiding mark-up based only on brand name.
EDIT: Just wanted to add, my perceptions on this have changed with time and experience. For example, I used to think that Savinellis were about the best you could do in that price range...but after acquiring a Luciano and smoking it for a while, I would definitely recommend them over a Sav. The difference has nothing to do with brand name or price, but simply the quality of materials and construction.