Thread does make a difference. After trying different threads, so far I prefer Aurifil 50wt for machine piecing and also for quilting on my domestic machine, and Glide trilobal polyester thread for frame quilting. Haven't done hand quilting in a long time. Aurifil is by far the best cotton thread I have used. I'm thinking the Presencia is probably even better, but haven't tried it yet (want to use up my old thread first).
I buy Aurifil online. Only a few quilt shops in my area carry it, and at a substantially higher price. I've never seen Presencia in a brick-and-mortar shop; when I buy it, that will be online also.
If you want to try Aurifil, I would suggest purchasing a spool through fabric.com (along with fabric, of course, to meet their minimum no-shipping fee!) or a single spool from eBay. Once I tried it, I was hooked. It is a very smooth and fine thread that leaves almost no lint in your machine.