Let $X$ and $Y$ be two smooth complex projective varieties. Then they are also symplectic manifolds. We know Gromov-Witten (GW) invariants are symplectic invariants. That means if there exists a a bijective symplectomorphism $f: X \to Y$, then GW invariants of $X$ and $Y$ are the same.
Now suppose $f: X \to Y$ is an algebraic isomorphism, or more generally, a birational map, then $f$ may not be a symplectomorphism. In this case, are GW invariants of $X$ and $Y$ different in general?