For me, there's only one pro to binding a quilt with a sewing machine--it's quick. The cons, however, are endless. For starters, the process is completely stressful. Days before I even start the binding I'm trying to get myself mentally prepared. I practice lots of exercises in deep breathing, a little music therapy, and as the time to begin gets closer, a motivating counseling session with myself in the mirror isn't unheard of.
After I've machine-sewn the binding to one side, I start to break out in a cold sweat, because I know it's about to get real. While I'm sewing the binding to the opposite side, I try to stare without blinking, because I know with one flinch my stitches will run up over the binding and all hope will be lost. It's very easy to mess up, and with all the time that is spent on a quilt, I don't want the last step to be the one that ruins it all.
I've tried many, many different methods to make my machine-binding look as good as possible: sewing it to the front and folding-it over and sewing to the back, sewing it on the back and folding it over toward the front, sewing through the front and back at the same time, sewing it to one side and then folding it over and sewing through both sides. Time and again I've tried to make my machine binding look professional, but I'm almost never happy with it. So, I finally decided to do something different.
I started hand-sewing my binding. I avoided trying it for a long time because I thought it would take too much time. Of course, it takes ALOT longer, but I absolutely love it. There's no crazy talk in the mirror, no cold-sweats, no stressful sewing--just me and the quilt watching TV together. The process is completely relaxing, and it looks worlds better when it's all done. I might not hand-sew the binding on every quilt in the future, but if time allows, I think it definitely worth the extra effort.

