Recent transformer-based ASR models have achieved word-error rates (WER) below 4%, surpassing human annotator accuracy, yet they demand extensive server resources, contributing to significant carbon footprints. The traditional server-based architecture of ASR also presents privacy concerns, alongside reliability and latency issues due to network dependencies. In contrast, on-device (edge) ASR enhances privacy, boosts performance, and promotes sustainability by effectively balancing energy use and accuracy for specific applications. This study examines the effects of quantization, memory demands, and energy consumption on the performance of various ASR model inference on the NVIDIA Jetson Orin Nano. By analyzing WER and transcription speed across models using FP32, FP16, and INT8 quantization on clean and noisy datasets, we highlight the crucial trade-offs between accuracy, speeds, quantization, energy efficiency, and memory needs. We found that changing precision from fp32 to fp16 halves the energy consumption for audio transcription across different models, with minimal performance degradation. A larger model size and number of parameters neither guarantees better resilience to noise, nor predicts the energy consumption for a given transcription load. These, along with several other findings offer novel insights for optimizing ASR systems within energy- and memory-limited environments, crucial for the development of efficient on-device ASR solutions. The code and input data needed to reproduce the results in this article are open sourced are available on [https://github.com/zzadiues3338/ASR-energy-jetson].