Long-form video processing fundamentally challenges vision-language models (VLMs) due to the high computational costs of handling extended temporal sequences. Existing token pruning and feature merging methods often sacrifice critical temporal dependencies or dilute semantic information. We introduce differential distillation, a principled approach that systematically preserves task-relevant information while suppressing redundancy. Based on this principle, we develop ViLAMP, a hierarchical video-language model that processes hour-long videos at "mixed precision" through two key mechanisms: (1) differential keyframe selection that maximizes query relevance while maintaining temporal distinctiveness at the frame level and (2) differential feature merging that preserves query-salient features in non-keyframes at the patch level. Hence, ViLAMP retains full information in keyframes while reducing non-keyframes to their most salient features, resembling mixed-precision training. Extensive experiments demonstrate ViLAMP's superior performance across four video understanding benchmarks, particularly on long-form content. Notably, ViLAMP can process ultra-long videos (up to 10K frames) on a single NVIDIA A100 GPU, achieving substantial computational efficiency while maintaining state-of-the-art performance. Code and model are available at https://github.com/steven-ccq/ViLAMP.