FWIW, I prefer my copper manifold. I strategically sweated certain spots so that it was solid when put together, but could easily be taken apart for cleaning. I have never had a stuck sparge, and have done several wheat beers without issue so far (rice hulls added always for good measure, however).
I also remember researching this topic, and came across an argument saying that with a braid (or improperly built manifolds), you can have uneven draining/rinsing of grains during sparging, which can decrease your efficiency. I don't know if this is a substantial factor in the home brewing setting, but something to consider with the braid. I remember that the argument swayed me enough to measure my manifold so that it was square, sat in the center of my tun, and has cuts placed for (relatively) even draining throughout the tun. I have had great success with my manifold, and routinely hit 86% +/- 1% efficiency.
I cannot say one way is better than another, but so far I have been very impressed with my copper manifold.
I think I may still have the drawn plans for what I did if you are interested.