What is your choice??
I have a friend that does beautiful quilts, when she is done with the quilting and trims the leftover batting and material she just runs it through the serger. Then sews the binding in the traditional way. When she's done her quilts always look great.
When I am ready to bind, I sew the binding on the front, trim the leftovers by hand, then finish the back by hand.
How do you do it? Do you like your binding full or a little flatter?