This study presents Strain Gradient Crystal Plasticity (SGCP) models within a thermodynamically consistent framework, formulated in terms of the MicroSlip and MicroCurl models. The MicroSlip SGCP model is based on the gradient of cumulative shear strain, while the MicroCurl model is formulated using the Nye tensor. The governing balance equations and the length scale are derived using the principle of virtual power and the Clausius-Duhem inequality. To solve both the classical and generalized balance laws, the Fast Fourier Transform (FFT) homogenization method is employed as an efficient computational approach. These balance laws are explicitly coupled within the FFT-based algorithm, ensuring an accurate numerical implementation. Shear band formation is categorized into two distinct types: slip bands and kink bands, characterized by the introduction of a rotation field. It is demonstrated that the Nye tensor accounts for the rotation field, leading to the conclusion that the MicroCurl SGCP model predominantly influences kink bands within the microstructure. In contrast, the MicroSlip SGCP model affects both slip and kink bands. Furthermore, the softening behavior is established for the single-crystal simulations and the results reveal that the conventional Crystal Plasticity (CCP) framework induces instability and voxel-dependent results. Notably, the MicroSlip SGCP model successfully mitigates these instabilities, producing voxel-independent (mesh-objective) results. Polycrystalline simulations are performed using both the MicroSlip and MicroCurl SGCP models, considering different length scales and higher-order interface conditions at grain boundaries. The results indicate that the SGCP models exhibit additional strain hardening compared to the CCP framework, which is attributed to the dislocation pile-up mechanism within the microstructure. Moreover, increasing the length scale enhances the hardening response and leads to a broader distribution of shear bands. The influence of different grain boundary conditions, MicroFree, MicroContinuity, and MicroHard, is also investigated. It is observed that under the MicroFree and MicroContinuity conditions, shear bands propagate across grain boundaries, whereas in the MicroHard condition, they terminate at the boundaries. This phenomenon may be associated with grain boundary embrittlement, potentially caused by oxidation or hydrogen dissolution.