I'm in agreement with Timber. Digging them with a backhoe will destroy the integrity of the side walls that woudl be just about impossible to re-gain.
The post hold digger will still have some soil around the post when you fill the hole, but the walls around the hole will provide all the stregth. Without those walls all the way around, you'll looking at failure. Especially if it rains and that fill material gets saturated.
Eddie