What exact bonuses are given when you are full?

What exact bonuses are given when you are full? Timmy (or Tommy, can't remember) briefly mentions that when you are full from eating, there seems to be more "oomph" or power in finding things and digging up stuff, but it's not exactly clear what those benefits entail. Is it:

• Increased chance to find loot?
• Increased chance for loot found to be more rare (like larger amounts of Bells)?
• Lesser substantial goodies like finding Bells from shaking trees?
• Etc.

I'm looking for, hopefully, exact benefits of staying at max full level. And if anything, want to know if being between 1-10 full level still yields benefits (ie, would being half full (5/10) still have more benefit than being hungry (1/10)?).

I've only seen being Full affect two things:

• Hitting a rock with an axe will consume 1 unit of fullness to break the rock. (This is not ideal if you're trying to farm the rock for resources)

• Using a shovel on a tree will consume 1 unit of fullness to dig up the entire tree, placing the whole thing in your inventory. It can then be replanted, fully grown.

So if you're not trying to do some landscaping, I haven't seen any benefit to eating at all.