Your question is if I understand correctly, whether we can think of a type that has a law abiding Eq instance that gives equality as fine grained as extensional equality (meaning structural equality?) but for which no law abing instance of Ord can be given such that a <= b && a >= b ==> a == b

This boils down to the question whether on each set with an equality relation defined on it a total ordering (consistent with the equality relation) can also be defined. One counterexample is the complex numbers.

Does that answer your question?

Cheers!