Personally~there is a place and time for both. I would plan on doing my first quilt with the machine. But I would as I got a nice collection of fabric to do some English paper piecing. Having a Grandmother's Flower garden in progress is wonderful if you have a bit of wait time everyday... you just grab the little bag of fabric, thread and needle and go.
Recently I met a man that did applique, all by hand, it was beautiful... I haven't mastered that, at all! :)