In this study, stress relaxation tests are performed to determine and compare the strain rate sensitivity of different titanium alloy microstructures using discrete dislocation plasticity (DDP) and crystal plasticity finite element (CPFE) simulations. The anisotropic α and β phase properties of alloy Ti-6242 are explicitly included in both the thermally-activated DDP and CPFE models together with direct dislocation penetration across material-interfaces in the DDP model. Equiaxed pure α, colony, Widmanstatten and basketweave microstructures are simulated together with an analysis of the effect of α grain size and dislocation penetration on rate sensitivity. It is demonstrated that alloy morphology and texture significantly influence microstructural material rate sensitivity in agreement with experimental evidence in the literature, whereas dislocation penetration is found not to be as significant as previously considered for small deformations. The mechanistic cause of these effects is argued to be changes in dislocation mean free path and the total propensity for plastic slip in the specimen. Comparing DDP results with corresponding CPFE simulations, it is shown that discrete aspects of slip and hardening mechanisms have to be accounted for to capture experimentally observed rate sensitivity. Finally, the dwell sensitivity in a polycrystalline dual-phase titanium alloy specimen is shown to be strongly dependent on its microstructure.