My theory is that dynamic verbs can take either more/most or better/best but the meaning will change.
I sleep more than him.
This means I sleep longer hours (quantity) than him.
I sleep better than him.
This means my sleep is of better quality than his.
Stative verbs can only take more/most.
I need water more than food.
Notice that you can't say:
I need water better than food.
But if I'm right, why can you say:
I know her better than you.
How can the quality of your knowing be good?