Gromov-Witten invariants can be interpreted as a (virtual) counting of curves on a complex projective variety, so they are biregular invariants.

However, they are not birational invariant in general. The behaviour of Gromov-Witten invariants under an arbitrary birational modification is in fact rather subtle. For more details and examples you can have a look at Section 1.4 of the paper

D. Abramovich, J. Wise Birational invariance in logarithmic Gromov-Witten theory, Compos. Math. 154, No. 3, 595-620 (2018). ZBL1420.14124.

On a complex projective variety, Gromov-Witten invariants can be interpreted as virtual counts of curves, so they are biregular invariants.

However, they are not birational invariant in general. The behaviour of Gromov-Witten invariants under an arbitrary birational modification is in fact rather subtle. 

For more details and examples you can have a look at Section 1.4 of the paper

D. Abramovich, J. Wise Birational invariance in logarithmic Gromov-Witten theory, Compos. Math. 154, No. 3, 595-620 (2018). ZBL1420.14124.