Manifolds distinguished by Gromov-Witten invariants?

The examples in Ruan's paper "Symplectic topology on algebraic 3-folds" (JDG 1994) seem to qualify: take any two algebraic surfaces V and W which are homeomorphic but such that V is minimal and W isn't. These are nondiffeomorphic, but VxS² and WxS² are diffeomorphic, and Ruan gives lots of examples (starting with V equal to the Barlow surface and W equal to the 8-point blowup of CP²) where the diffeomorphism can be arranged to intertwine the first Chern classes, whence by a theorem of Wall the almost complex structures are isotopic. However, the distinction between the GW invariants between V and W (which holds because V is minimal and W isn't) survives to VxS² and WxS², so VxS² and WxS² aren't symplectic deformation equivalent.

Here is an answer to the REFINED question given to me by Richard Thomas. In this refined version one looks for an example such that the cohomology classes of two symplectic forms coincide.

In a later paper 1996, Duke Vol. 83 TOPOLOGICAL SIGMA MODEL AND DONALDSON TYPE INVARIANTS IN GROMOV THEORY, Ruan proved that such refined examples exist. He says in this paper that for product examples $V\times S^2$ from the paper in JDG 1994 (cited by Mike Usher) he does not know whether the classes of constructed symplectic forms can coincide as well. In fact this does not seem very plausible.

These refined examples are two $3$-dimensional Calabi-Yau manifolds, constructed by Mark Gross. The construction is described in the paper of Mark Gross (1997): "The deformation space of Calabi-Yau $n$-folds with canonical singularities can be obstructed". One $3$-dimensional Calabi-Yau is a smooth anti-canonical section of $\mathbb CP^1\times \mathbb CP^3$ and the over is a smooth anti-canonical section of the projectivsation of the bundle $O(-1)+O+O+O(1)$ over $\mathbb CP^1$.

The construction of Gross is recalled on pages 47-48 of http://xxx.soton.ac.uk/PS_cache/math/pdf/9806/9806111v4.pdf

Using Wall's theorem Ruan proves that these Calabi-Yau manifolds are differomorphic. Then he studies the quantum cohomology rings of these Calabi-Yaus and proves that they are different.