A long standing conjecture says that two simply connected nilpotent Lie groups are quasi-isometric if and only if they are isomorphic. A seminal result of Pansu reduces the problem of pairs of such groups with isomorphic Carnot-gradable Lie groups. In a joint work with Claudio Llosa Isenrich and Gabriel Pallier, we show that such pairs can have different Dehn functions. We deduce that the Dehn function is not an invariant of the asymptotic cone. As an application we answer a question of Cornulier on a natural variant of the above conjecture.