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As the size of biomedical implants and wearable devices becomes smaller, the need for methods to deliver power at higher power densities is growing. The most common method to wirelessly deliver power, inductively coupled coils, suffers from poor power density for very small-sized receiving coils. An alternative strategy is to transmit power wirelessly to magnetoelectric (ME) or mechano-magnetoelectric (MME) receivers, which can operate efficiently at much smaller sizes for a given frequency. This work studies the effectiveness of ME and MME transducers as wireless power receivers for biomedical implants of very small (<2 mm3) size. The comparative study clearly demonstrates that under existing safety standards, the ME architecture is able to generate a significantly higher power density than the MME architecture. Analytical models for both types of transducers are developed and validated using centimeter scale devices. The Institute of Electrical and Electronics Engineers (IEEE) and the International Commission on Non-Ionizing Radiation Protection (ICNIRP) standards were applied to the lumped elements models which were then used to optimize device dimensions within a 2 mm3 volume. An optimized ME device can produce 21.3 mW/mm3 and 31.3 W/mm3 under the IEEE and ICNIRP standards, respectively, which are extremely attractive for a wide range of biomedical implants and wearable devices.