We describe a family of finitely presented groups which are quasi-isometric but not bilipschitz equivalent. The first such examples were described by the first author (Duke Math. J., 2010) and are the lamplighter groups F \wr Z where F is a finite group; these groups are finitely generated but not finitely presented. The examples presented in this paper are higher rank generalizations of these lamplighter groups and include groups that are of type F_n for any n.

The first author acknowledges support from National Science Foundation grant DMS-1207296. The third author acknowledges support from National Science Foundation grant DMS-1105407.