I have done it both ways. It depends how you plan to quilt it. I typically applique before cutting my pieces because applique causes the fabric to slightly shrink the background fabric. Heavy starch & a tear away stabilizer help some, but it's inevitable that there will be some shrinkage. I find I get less shrinking with hand applique than with machine applique so if you plan to machine applique it, I'd definitely do that first so you have the opportunity to re-block your top before quilting it. With hand applique, it is not easy to get your needle in & out of the middle of your sandwich on curved edges; my stitches always end up sloppier when I try, so I typically make sure to add all applique before I start quilting. Plus, my needles get bent quite quickly when working with a quilted sandwich because I can't see & I'm trying to only go halfway down. The other advantage is that when you are quilting, you can quilt around the "ditch" of the applique to make it puff up & do your filler around it. Looks super cute & then you can see the outline of the butterfly both front & back.
On the other hand, if you plan to take it to a LA for panto design, then yes, I'd do the applique later & I'd do it by hand.
Last edited by Bree123; 04-10-2016 at 12:52 PM.