This paper presents an accurate comparison between the performance of inductive and ultrasonic links for wireless power transmission (WPT) to biomedical implants with different sizes and implantation depth. These links' performances are evaluated based on the power transmission efficiency (PTE) at their optimized operation frequency (fp) to find out which WPT method is more efficient and robust. The geometry of several sets of inductive and ultrasonic links along with their fp have been optimized for different separation distances (d12) between the transmitter (Tx) and receiver (Rx) and two Rx diameters (D02) to achieve the highest PTE. The simulation results show that the ultrasonic link outperforms the inductive link when the Rx has D02 of 1.2 mm and implanted deep inside the tissue. However, for an Rx with the D02 of 5 mm and above, the inductive link achieves higher PTE, particularly at shorter d12 of 5 mm (46% vs. 40%) and 10 mm (40% vs. 28%). The simulated misalignment results show that the ultrasonic link is more prone to misalignments greater than 1 mm compared to its inductive counterpart.