This paper explores the impact of back-to-back converter control strategies on the torsional dynamics of grid-forming permanent magnet synchronous generator wind turbines (GFM-WTs). Two general converter control methods for GFM-WTs, distinguished by the placement of dc-link voltage control (DVC)-either in the machine-side converter or the grid-side converter, are evaluated through the complex torque coefficient method to offer a theoretical basis. It reveals that a negative damping is introduced when the DVC is with the machine-side converter. Then, to further characterize the parametric impacts of electrical and mechanical system constants and controller gains, the sensitivity analysis is performed by employing the partial derivative algorithm, which is based on the feedforward neural network training. It is found that the converter control has a limited impact on the damped frequency in both GFM converter control methods. Finally, electromagnetic simulations based on full-order nonlinear models of GFM-WTs are carried out to confirm the theoretical findings.