A part from a possible loss in performance, is there any advantage to running NPT simulations with v-rescale instead of doing also NPT but with stochastic dynamics (working as a thermostat). I guess maybe SD affects dynamical properties like diffusion but what about other properties?
The formulation of your questions in confusing. Do you think v-rescale is slower than SD?
The SD integrator is slower than MD with leap-frog and a v-rescale thermostat. Both give the correct ensemble. But as you say, SD affects dynamical properties and slows down all slow dynamical modes. The only advantage of SD is quick equipartitioning of kinetic energy. Theoretically there is also less communication since you do not need to reduce the kinetic energy over MPI ranks, but in practice this is negligible, especially with nsttcouple set to 10.
If your system is fully overdamped and your friction for SD is lower than the damping in the system, the sampling speed might not be affected much. This is the case for e.g. solvation free-energies for small molecules, where you need SD to sample the decoupled state correctly. For larger systems there might or might not be a measurable effect.