Video technology is advancing toward Ultra High Definition (UHD) and High Dynamic Range (HDR), which intensifies the need for higher compression efficiency for these high-specification videos. Beyond advances in traditional codecs, neural video codecs (NVCs) have attracted significant research attention and have evolved rapidly over the past few years. The coding artifacts of NVCs often exhibit content-varying and generative characteristics, which differ from those of conventional codecs and are challenging for traditional video quality assessment (VQA) methods to capture. Therefore, VQA metrics are required to generalize across different codecs, content types, and dynamic ranges to better support video codec research and evaluation. In this paper, we propose FDIM, a feature-distance-based generic video quality metric for both traditional and neural video codecs across SDR and HDR formats. FDIM employs a hybrid architecture that integrates deep and hand-crafted features. The deep feature component learns multi-scale representations to capture distortions ranging from structural and textural fidelity degradation to high-level semantic deviations, while the hand-crafted feature component provides stable complementary cues to improve overall generalization. We trained FDIM on a large-scale subjective quality assessment dataset (DCVQA) consisting of over 16k video sequences encoded by traditional block-based hybrid video codecs and end-to-end perceptually optimized neural video codecs. Extensive experiments on ten SDR/HDR VQA datasets containing diverse, previously unseen codecs demonstrate that FDIM achieves strong generalization and high correlation with subjective assessment. The source code for FDIM and the DCVQA validation set will be released at https://github.com/MCL-ZJU/FDIM.