The emerging reflecting intelligent surface (RIS) technology promises to enhance the capacity of wireless communication systems via passive reflect beamforming. However, the product path loss limits its performance gains. Fully-connected (FC) active RIS, which integrates reflect-type power amplifiers into the RIS elements, has been recently introduced in response to this issue. Also, sub-connected (SC) active RIS and hybrid FC-active/passive RIS variants, which employ a limited number of reflect-type power amplifiers, have been proposed to provide energy savings. Nevertheless, their flexibility in balancing diverse capacity requirements and power consumption constraints is limited. In this direction, this study introduces novel hybrid RIS structures, wherein at least one reflecting sub-surface (RS) adopts the SC-active RIS design. The asymptotic signal-to-noise-ratio of the FC-active/passive and the proposed hybrid RIS variants is analyzed in a single-user single-input single-output setup. Furthermore, the transmit and RIS beamforming weights are jointly optimized in each scenario to maximize the energy efficiency of a hybrid RIS-aided multi-user multiple-input single-output downlink system subject to the power consumption constraints of the base station and the active RSs. Numerical simulation and analytic results highlight the performance gains of the proposed RIS designs over benchmarks, unveil non-trivial trade-offs, and provide valuable insights.