Deploying Large Language Models (LLMs) on mobile devices enhances privacy and reduces latency, but is severely constrained by hardware inefficiencies. We present the first comprehensive, cross-layer measurement study of mobile LLM inference, spanning five mainstream frameworks (e.g., llama.cpp and GENIE) and three hardware backends (CPU, GPU, and NPU). To enable this analysis, we develop PowerBench, a fine-grained profiling tool that measures LLM throughput and provides the first backend-specific energy attribution for mobile LLM inference, going beyond traditional device-level measurements. We further conduct hardware microbenchmarks to characterize the memory-system performance and compute capabilities of mobile CPUs, GPUs, and NPUs. Our study yields three critical insights: (1) Framework-induced performance gaps are substantially amplified on NPUs, reaching up to $10\times$ due to differences in offloading strategies, hardware-underutilizing operators, and activation quantization strategies. (2) We identify a distinct ``phase split,'' in which NPUs excel at compute-bound prefilling, while CPUs outperform all other backends in memory-bound decoding. This split is driven by NPUs' preference for large, fixed-shape workloads, which conflicts with the small-kernel, dynamic nature of decoding. (3) Backend-specific profiling uncovers substantial scheduling headroom missed by prior work. Suboptimal thread configurations, uncoordinated NPU sleep latencies, and CPU polling intervals result in unnecessary energy consumption. For example, tuning CPU frequency alone reduces energy consumption by up to $39.7\%$. Leveraging these findings, we estimate that an energy-oriented configuration can reduce energy consumption by up to $53.2\%$ on the NPU backend across three datasets, highlighting the substantial potential for further efficiency improvements in mobile LLM deployment.

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