Enlarged perivascular spaces (PVS) are increasingly recognized as biomarkers of cerebral small vessel disease, Alzheimer's disease, stroke, and aging-related neurodegeneration. However, manual segmentation of PVS is time-consuming and subject to moderate inter-rater reliability, while existing automated deep learning models have moderate performance and typically fail to generalize across diverse clinical and research MRI datasets. We adapted MedNeXt-L-k5, a Transformer-inspired 3D encoder-decoder convolutional network, for automated PVS segmentation. Two models were trained: one using a homogeneous dataset of 200 T2-weighted (T2w) MRI scans from the Human Connectome Project-Aging (HCP-Aging) dataset and another using 40 heterogeneous T1-weighted (T1w) MRI volumes from seven studies across six scanners. Model performance was evaluated using internal 5-fold cross validation (5FCV) and leave-one-site-out cross validation (LOSOCV). MedNeXt-L-k5 models trained on the T2w images of the HCP-Aging dataset achieved voxel-level Dice scores of 0.88+/-0.06 (white matter, WM), comparable to the reported inter-rater reliability of that dataset, and the highest yet reported in the literature. The same models trained on the T1w images of the HCP-Aging dataset achieved a substantially lower Dice score of 0.58+/-0.09 (WM). Under LOSOCV, the model had voxel-level Dice scores of 0.38+/-0.16 (WM) and 0.35+/-0.12 (BG), and cluster-level Dice scores of 0.61+/-0.19 (WM) and 0.62+/-0.21 (BG). MedNeXt-L-k5 provides an efficient solution for automated PVS segmentation across diverse T1w and T2w MRI datasets. MedNeXt-L-k5 did not outperform the nnU-Net, indicating that the attention-based mechanisms present in transformer-inspired models to provide global context are not required for high accuracy in PVS segmentation.