I bind all my quilts with bias binding that I make myself. I've learned that 2-3/4" is the best width for general use. When I make a narrower binding it's always because I don't have enough fabric to make it wider and I usually wish for something a bit wider. It all depends on the fluffiness of the quilt.
I also agree that for a lot of curves a narrower binding would work better. Keep the wide binding that you bought and make your own for the apple quilt. It's easy peasy with pressing it in half being the most tedious step.