For small pieces (1/4 inch, up to maybe 2 inches on a side) I use English paper piecing because it controls any bias stretch/distortion. Machine sewing such short seams would really not suit me. I also think a whip stitched seam (EPP) will have a bit more give than a running stitch (traditional hand piecing), so the threads are less likely to break after the quilt is done. Hundreds of years of quilting tradition probably disagree with me on that point, but I'm more comfortable with EPP.
For larger pieces I would use my machine. I'm not afraid of y-seams, but many people find them easier to manage by hand than on machine.
Ultimately, the method you use is should be whatever works best for you. I know I've read blogs and QB posts by people that do this type of piecing by hand without papers; if that suits you, then go for it!