How about a combination of the techniques? Applique the larger parts and embroider the smaller ones. There's no rule, that says you have to use only one method.
I would use Heat & Bond Lite, for the applique. Draw design onto the H&B paper, cut out, then iron onto fabric. Cut fabric around the shape, leaving 1/4" - 3/8", for turning. Clip curves well. Remove paper and with just the TIP of your iron, gently nudge the fabric edges over, onto the H&B, making as smooth a turn, as possible. Be careful to not go past the fabric, when pressing. After the edges are turned, press shape into place, on block. I like to use a blanket stitch around the edge but use whatever looks/feels best. Just make sure you get the very edge, somewhere in your stitching.
Then you can embroider the eyes, antennae, etc.
