Suppose I have a racket that can support both 1-piece and 2-piece stringing, and I want to string it up with only one type of string (no hybrid), what are the pros/cons in terms of playability with each method? I realize that 1-piece is a little more difficult to string, having to pull the longer piece through the holes.
I am thinking in terms of playability. Does one method result in the racquet feeling tighter than it really is? Does one way better ensure tension maintenance? Could it affect the size of the sweet spot?
As you've now discovered, there are a lot of opinions on the differences and benefits of each, and quite a bit of mythology as well. In fact, there isn't that much difference in practical playing terms, and there are stringing advantages to each. While one piece does require you to pull a longer piece through part of the racquet, it's actually not much of a factor, since it's really only on half of the mains, and you don't even have to weave those. As long as you keep track of your long end while you do the mains, you'll be fine. Once you start the crosses, it's essentially the same length of string you'd be handling anyway. The plus side for one piece is that you do two fewer knots.
Generally most racquets have either a recommended pattern (sometimes one piece, sometimes two), or have a correct way to do both. Consult the recommendation for your particular frame. The only caveat is that it's accepted wisdom that you don't want to do a one piece job if it will make you install the mains from the bottom up. Otherwise, do whichever recommended pattern you prefer.
As for playability, you will NOT be able to tell the difference, assuming you do each string job well. The tiny differences in one outside main and/or the extra tie offs will be negligible. Tension maintenance will be almost exactly the same...there can be a slight edge to the one piece job, but not enough to matter. And anyone who tells you they can feel the difference in the sweet spot is kidding himself/herself or not doing the best job possible with one or both method.