Toric symplectic manifolds contain an interesting and well-studied family of Lagrangian tori, called toric fibres. In this talk, we address the natural question of which toric fibres are equivalent under Hamiltonian diffeomorphisms of the ambient space. On one hand, we use a symmetric version of McDuff's probes to construct such equivalences and on the other hand, we give certain obstructions coming from Chekanov's classification of product tori in symplectic vector spaces combined with a lifting trick from toric geometry. We will discuss many four-dimensional examples in which a full classification can be achieved.