Figure-8 is the strongest, followed by overhand, followed by girth-hitch.
Ropes are weakened when you bend them. Â The more you bend them, the weaker they are. Â A figure-8 bends the rope less than an overhand, which bends the rope less than a girth hitch. Â
Additionally with a girth hitch, the doubling back of the cord effectively makes it a 2-1 pulley - which doubles the force on the cord (minus frictional forces).
Another con against the girth is that it is not redundant.
With that said, I don't particularly care for the rig depicted in the picture as the helper knot against the tree is roughly perpendicular to the direction of the pull. Â This Â weakens the system and the knot doesn't really add anything to it. Â Kind of like when you set up an anchor with 2 pieces far apart. This effect would be lessened if the helper knot was further from the tree. Â I personally, skip this knot, and just use a figure-8. Â Quicker, stronger, redundant. Â I will occasionally use girth hitches when I need some extra distance out of my cordelette.
Then again cordelette are pretty over designed and I don't think any of these scenarios are likely to fail.