So much depends on which applique method you use!
For fusible, I use either a blanket stitch (with doubled regular thread or single thicker thread so it shows more) or a satin stitch.
Mostly, though, I do freezer paper applique a la Harriet Hargrave. For that I use the blanket stitch with a much smaller stitch length and "bite". Some people prefer a small zigzag for that.
I have tried the dryer sheet method where you sew around the outside, slit the dryer sheet, and turn the applique right side out. It works well for larger shapes that have fairly large curves to them. I found it difficult for smaller applique shapes -- less definition and accuracy than I like. Since that is a turned applique method, I would probably use blanket stitch on it.
Satin stitch adds a lot of bulk to a turned edge, so it is probably more suitable for fusible applique than turned edge applique, although it could be used for both.