This is actually an old mystery because the DNA-binding specificities of different HOX proteins, determined using biochemical approaches, are remarkably similar.  How can they regulate different genes if they all bind the same site?  Well, it looks like they don’t all bind the same sites.  This paper in EMBO Journal shows that different HOX proteins associate with different genomic regions in vivo.  How they end up there is still not understood, but presumably it depends on the specific interactions between the HOX proteins and other TFs that DO recognize different DNA sequences.  This is a very intriguing paper – take a look.