I used to think one could "feel" the difference. I bought two different quilt backings at the LQS, one I thought felt so very nice, the other, meh, but it was a small quilt I planned to give away and didn't want to invest a lot. Washed them both and my opinion changed drastically. The nice one was rough and scratchy, the meh had softened and was smooth.
I have rarely found decent fabric at the local wally world. The next big box fabric store is an hour away, I get there about once a year. When i can, my preference is LQS or online, name brand bolt.