wigwamitus
If your area is relatively flat like in the images, even a bit more hilly the leveling base is more stable than the Anvil. You can make it work for high angle shooting, but there is a time penalty over the Anvil 30 because you' have to adjust one leg height.
Stability it goes like this (least to most stable): BH40 > Anvil 30 > Leveling Base
Weight it (heaviest to lightest): BH40 > (Leveling Base=Anvil 30)
Transport Bulkiest to most compact: BH40 > Leveling Base > Anvil 30
Flexibility of mounting options without modification: (Leveling Base=BH40) > Anvil 30
Personal (only) observations in operation:
Leveling Base:
I find the leveling base easier to control, a bit easier add downward weight between the tripod and faster to get the perfect tension I want and it will tend to stay on target better.
Anvil 30:
With the Anvil 30 I also have the needed concern not to release the wrong lever - the levers are very different in size - but the are both levers and they are on the wrong side for a left handed shooter so we shoot them backwards on the support side.
BH40:
If I was really concern about the perfect pan shot, this might be the way to go. But I have yet to see the animals I hunt every run perfectly level perpendicular to my setup. - the other two work just fine.
All that said, I am using the Anvil 30 - but there are times when I miss the leveling base seating at home.