I agree with using fine thread for piecing. I have experimented with cotton and poly, both alone and together. I find that poly, even when used only in the bobbin, does not give me as flat a seam as cotton. So my personal favorite for piecing is Aurifil 50wt cotton in both top and bobbin. (I would also use Presencia 60wt; just don't have any on hand.)
For quilting, what matters is how you like the look. I have found over time that, for the kind of quilting I do, I do not particularly care for look of the heavier weight cottons (such as King Tut). On my domestic machine, I do like the look of Aurifil 50wt cotton. That thread is not strong enough for my Voyager midarm (frame) machine, however. After trying out several threads with the Voyager, I have settled almost exclusively on Glide polyester thread. It adds a little sparkle to my quilts (of which they are in desperate need most times!), it suits my close quilting style, and it *never* shreds or breaks on me.