Aerial base stations (ABSs) have emerged as a promising solution to meet the high traffic demands of future wireless networks. Nevertheless, their practical implementation requires efficient utilization of limited payload and onboard energy. Understanding the power consumption streams, such as mechanical and communication power, and their relationship to the payload is crucial for analyzing its feasibility. Specifically, we focus on rotary-wing drones (RWDs), fixed-wing drones (FWDs), and high-altitude platforms (HAPs), analyzing their energy consumption models and key performance metrics such as power consumption, energy harvested-to-consumption ratio, and service time with varying wingspans, battery capacities, and regions. Our findings indicate that FWDs have longer service times and HAPs have energy harvested-to-consumption ratios greater than one, indicating theoretically infinite service time, especially when deployed in near-equator regions or have a large wingspan. Additionally, we investigate the case study of RWD-BS deployment, assessing aerial network dimensioning aspects such as ABS coverage radius based on altitude, environment, and frequency of operation. Our findings provide valuable insights for researchers and telecom operators, facilitating effective cost planning by determining the number of ABSs and backup batteries required for uninterrupted operations.