Besides using a type of thread that your sewing machine likes (my machine is exclusive to Aurifil these days) the other really important choice is what type of needle to use.
I use a different needle for quilting and for piecing. I know a few people who never change their needle until it breaks - I'm looking at you Louise!! LOL
I always change my machine quilting needle after quilting every large quilt, or after 2 or 3 small quilts. It is really important when your needle is making thousands of stitches through 3 layers of materials at a high rate of speed to have a sharp needle. Needles that develop spurs or become slightly bent can result in costly machine repairs. Needles are cheap but sewing machine repairs are not!
Here's my tip: place the needle container near your machine so you always know what type of needle you're using. You can see on the little ledge on the right side of my machine that I have my Schmetz Topstitch needle case there (and you can see that it's empty because I go through a lot of needles). It's a visual reminder to me of the type of needle that's currently in the machine. If I want to stop quilting and start piecing, I would want to change the needle. For precision piecing, especially with tiny pieces, I prefer the Microtex Sharp needles.
Yes there is a difference!
If you have problems with tension, skipped stitches or thread breakage, I would encourage you to try a new and/or a different kind of needle.
It has been a long time since I stipple quilted anything. It's one of the quickest and easiest quilting designs to use and since the baby quilt has to be finished, it got stippled. And look at that... the binding is prepped and ready to go on!