Structured pruning is widely used to compress large language models (LLMs), yet its effectiveness depends heavily on neuron importance estimation. Most existing methods estimate neuron importance from activation statistics on a single calibration dataset, which introduces calibration bias and degrades downstream cross-task generalization. We observe that neurons exhibit heterogeneous distribution sensitivity, with distribution-robust neurons maintaining consistent rankings across datasets and distribution-sensitive neurons showing high cross-dataset ranking variance. Based on this, we identify two structural limitations in existing methods. First, ranking all neurons within a shared space causes distribution-sensitive neurons that strongly activate on calibration inputs to dominate, crowding out distribution-robust neurons critical for out-of-distribution tasks. Second, applying activation-based importance metrics uniformly can be unreliable. Distribution-sensitive neurons that infrequently activate on calibration data receive insufficient activation signal for accurate local ranking. To address these limitations, we propose GPrune-LLM, a generalization-aware structured pruning framework that explicitly accounts for neuron differences in cross-distribution behavior. We first partition neurons into behavior-consistent modules to localize ranking competition, then evaluate activation-based metric reliability per module according to distribution sensitivity and score magnitude. For modules where activation-based scoring is unreliable, we switch to an activation-independent metric. Finally, we adaptively learn module-wise sparsity. Extensive experiments across multiple downstream tasks demonstrate GPrune-LLM's consistent improvements in post-compression generalization, particularly at high sparsity, and reduced dependence on importance metric choice.