A linearized sensitivity and stability analysis of fiber spinning of semi-crystalline polymers has been carried out for both low- and high-speed spinning conditions to investigate the relative roles of flow-enhanced crystallization (FEC) and thermal-induced crystallization (TIC) on the process dynamics. The analysis is based on an earlier-developed two-phase constitutive model for FEC that utilizes either the Giesekus or the Extended Pom-Pom constitutive equations for the amorphous phase and a rigid-rod model for the semi-crystalline phase, combined with the transport balances for the 1-D fiber spinning model. Model parameters from fits of the steady-state low- and high-speed spinning of Nylon and L-polylactic acid are used to illustrate the effects of changes in various process variables (principally air cooling rate and temperature) on the system sensitivity. Results show that higher crystallization, whether from TIC or FEC, generally equates to lower spinline sensitivity. However, factors such as high-speed necking induced by FEC, viscoelastic stresses, and thermal transport properties are also shown to impact trends in the sensitivity. Because of the specific nature of the FEC model and lack of a general theory for determining model parameters from first principles, calculations and conclusions are necessarily system specific.