I think that the "above-the-device" crowd has a fair argument on it being slightly easier to set up. And since ease of setup and speed could be factors in deciding to use a backup, that might make it safer. Like how if your helmet is heavy and uncomfortable, you won't wear it, even if it offers great protection, and is thus less safe than a light, comfortable one that you actually wear.
It's also easier to take an unknown setup (a different harness, borrowing someone else's cord, etc) and make it work.
But the main advantage of the "below-the-device" argument is, for me, that if you let go of your brake then it uses the device itself to add friction and stop you, vice simply using the knot's own friction properties. That, and the "I'm falling, I'll grab the rope" instinct which would negate the benefit in the "above-device" setup, but would strengthen your brake grip in the "below device" setup means that I vote in favor of using it below the device.
I'm also definitely in favor of extending the device in all raps.
That said, I generally don't do a backup when I'm not first on the rope. But I know I should.