Examples of "non equivalent" algebras that are derived equivalent?

One can define different equivalence relations between algebras depending on what one want to study, but also these definitions may have their own life and not result as one expected at first.

My interest is in derived equivalence. Which is your favorite example of two algebras A and B such that D(A) is triangulated equivalent to D(B) but one feel that they are really ”different”? Maybe another way to formulate the question is: what is your favorite invariant that ”should be” derived invariant but it is not?

My personal example is an algebra A with finite global dimension, and B another algebra derived equivalent to A but with different global dimension. Do someone has any other ”example” of ”non-equivalent” algebras A and B that are still derived equivalent?