You cannot look only at the wt of the thread. Regular cotton thread is 50wt 3-ply. I find that this 3-ply thread takes up too much of the seam allowance. I get more accurate piecing by using Aurifil 50wt 2-ply thread. In addition to thread weight, you must also look at plys and also at composition of the thread. I prefer cotton thread for piecing because it "grabs" better than slick polyester threads. Aurifil is a good brand because the thread is very smooth, leaving less lint in your machine than many other cotton threads.
I have used regular 50wt 3-ply thread to quilt with. It is fine as long as your quilting lines are a moderate distance apart. If you do a lot of close quilting with this thread, you will find that this thread will stiffen your quilt quite a bit. For quilting I prefer a polyester thread to cotton for several reasons -- it is stronger, it does not dry rot over time, and it will not stiffen a quilt as much as cotton thread. My favorite is Glide thread, although Sigma from metroemb.com is supposed to be very similar (and much cheaper, especially if purchased during one of their 50% off sales). For a cotton thread that will blend for quilting, I again like Aurifil 50wt 2-ply. These 2 threads do not make my quilt stiff even if I go hog-wild and quilt in little loops all over the surface.
For my initial years of quilting, I have to admit that thread did not seem important to me and I used mostly 50wt 3-ply. In the last few years, however, I have realized that thread quality does make a difference to me. I think this is a common progression in quilters.