Abstract. Let (M,C) be an oriented 3-manifold with a cooriented contact structure. Clearly every Legendrian knot in (M,C), i.e. a knot that is everywhere tangent to C, has the natural framing induced by the coorienting vector field V_C of C.
Recently Fuchs and Tabachnikov used the Kontsevich integral universal Vassiliev invariant to prove that the groups of complex-valued Vassiliev invariants of Legendrian and of framed knots are canonically isomoprhic when the ambient contact manifold is \R^3 with the standard contact structure. We show that for any Abelain groups \mathcal A the groups of \mathcal A-valued Vassiliev invariants of framed and of Legendrian knots are canonically isomorphic for a vast collections of contact 3-manifolds (M,C), where the Kontsevich integral is not known to exist. This class of contact 3-manifolds (M,C) includes all hyperbolic M, all tight C, and all the cases where the Euler class of C is in the torsion of H^2(M).
On the other hand we construct the first examples of contact 3-manifolds where Vassiliev invariants of Legendrian and of framed knots are different and Vassiliev invariants of Legendrian knots actually do distinguish Legendrian knots that realize isotopic framed knots.
A knot K is said to be Pseudo-Legendrian in (M,V_C) if it is nowhere tangent to V_C. Clealry every Legendrian knot in (M,C) is Pseudo-Legendrian in (M,V_C). Benedetti and Petronio conjectured that the groups of \mathcal A-valued Vassiliev invariants of Legendrian knots from (M,C) and of Pseudo-Legendrian knots from (M,V_C) are canonically isomorphic.
We show that these groups are indeed canonically isomoprhic In particular this result implies that the only information about a Legendrian knot that can be captured with Vassiliev invariants of Legendrian knots is the Pseudo-Legendrian isotopy class of the Legendrian knot.