  We show that for a large class of contact 3-manifolds the groups of Vassiliev
invariants of Legendrian and of framed knots are canonically isomorphic. As a
corollary, we obtain that the group of finite order Arnold's $J^+$-type
invariants of wave fronts on a surface $F$ is isomorphic to the group of
Vassiliev invariants of framed knots in the spherical cotangent bundle $ST^*F$
of $F$.
  On the other hand we construct the first examples of contact manifolds for
which Vassiliev invariants of Legendrian knots can distinguish Legendrian knots
that realize isotopic framed knots and are homotopic as Legendrian immersions.
