Upper limb robotic (myoelectric) prostheses are technologically advanced, but challenging to use. In response, substantial research is being done to develop person-specific prosthesis controllers that can predict a user's intended movements. Most studies that test and compare new controllers rely on simple assessment measures such as task scores (e.g., number of objects moved across a barrier) or duration-based measures (e.g., overall task completion time). These assessment measures, however, fail to capture valuable details about: the quality of device arm movements; whether these movements match users' intentions; the timing of specific wrist and hand control functions; and users' opinions regarding overall device reliability and controller training requirements. In this work, we present a comprehensive and novel suite of myoelectric prosthesis control evaluation metrics that better facilitates analysis of device movement details-spanning measures of task performance, control characteristics, and user experience. As a case example of their use and research viability, we applied these metrics in real-time control experimentation. Here, eight participants without upper limb impairment compared device control offered by a deep learning-based controller (recurrent convolutional neural network-based classification with transfer learning, or RCNN-TL) to that of a commonly used controller (linear discriminant analysis, or LDA). The participants wore a simulated prosthesis and performed complex functional tasks across multiple limb positions. Analysis resulting from our suite of metrics identified 16 instances of a user-facing problem known as the "limb position effect". We determined that RCNN-TL performed the same as or significantly better than LDA in four such problem instances. We also confirmed that transfer learning can minimize user training burden. Overall, this study contributes a multifaceted new suite of control evaluation metrics, along with a guide to their application, for use in research and testing of myoelectric controllers today, and potentially for use in broader rehabilitation technologies of the future.