This study presents a systematic comparison of two dominant paradigms for improving rotation robustness in remote sensing semantic segmentation: rotation-invariant architectural modules (represented by Rotation-Invariant Channel Mapping, RICM) and random rotation data augmentation. Despite both approaches being widely adopted, a fair and side-by-side evaluation under unified experimental conditions remains lacking. Using U-Net as the baseline on the LoveDA dataset, we comprehensively evaluate six strategies: RICM alone, random rotation augmentation at probabilities $p=0.25$ and $p=0.5$, and their combinations. Performance is assessed under both discrete rotations (0°, 90°, 180°, 270°) and continuous angles (0°–180° with 15° intervals), supplemented by Rotation Consistency (RC) analysis, class-wise evaluation, and computational cost comparison. Cross-dataset validation on ISPRS Potsdam confirms generalizability. Our results demonstrate that: (1) random rotation augmentation consistently outperforms RICM, delivering substantial robustness gains with zero inference overhead; (2) augmentation probability controls a clear accuracy–robustness trade-off, with $p=0.25$ achieving the best balance (maintaining 0° mIoU at 74.8% while boosting 90° mIoU from 54.9% to 63.1%) and $p=0.5$ achieving near-invariance at the cost of reduced baseline accuracy; and (3) RICM offers only marginal benefits and becomes redundant when augmentation is applied. Analysis of the observed performance patterns suggests that early-stage RICM insertion may suppress useful orientation-specific features and that its rotation-ensemble averaging may be insufficient for dense prediction tasks. Overall, random rotation augmentation proves to be a simple, effective, and computationally efficient strategy for improving rotation robustness in remote sensing segmentation.