Knowledge Distillation (KD) has emerged as a crucial technique for compressing Large Language Models (LLMs). Although existing cross-tokenizer KD methods have made notable progress, their effectiveness remains constrained by suboptimal alignment across sequence and vocabulary levels. To address these limitations, we introduce Dual-Space Weighting and Time-Warped Alignment (DWA-KD), a novel cross-tokenizer distillation framework that enhances token-wise distillation through dual-space entropy-based weighting and achieves precise sequence-level alignment by leveraging both lexical and semantic information. At the token level, DWA-KD maps teacher representations into the student space and vice versa, performing dual-space KD via Kullback–Leibler divergence (KL). The process is modulated by dual-space entropy-based weights that up-weight tokens where the student is uncertain and the teacher is confident, thereby focusing learning on informative tokens rather than treating all positions equally. At the sequence level, DWA-KD applies Soft Dynamic Time Warping (Soft-DTW) to both the embedding and final hidden-state layers, enabling robust alignment of lexical and contextual semantics between teacher and student sequences. Extensive experiments across diverse NLP benchmarks demonstrate that DWA-KD consistently outperforms state-of-the-art KD baselines, while ablation studies confirm the complementary contributions of entropy-based token weighting and embedding and final hidden state layer Soft-DTW alignment.