A significant percentage of the offshore wind resource is located in waters deeper than 60m. Therefore, several floating offshore wind turbines (FOWT) have been conceived in recent years. In deep waters, it seems logical to also harvest wave energy. One of the options to harness both resources is to use a floating offshore hybrid wind-wave energy converter (FOHWWEC), which physically combines a FOWT with a wave energy converter (WEC). Different studies have addressed the functionality, feasibility, optimization, control and survivability of FOHWWEC concepts. The majority considers a proven FOWT substructure to fit a certain type of WEC. Dynamic analyses in both, frequency and time domains, and laboratory experiments with models have been done. Nevertheless, the investigated studies have not considered the FOHWWEC concept as part of an extensive design space. In other words, they have not attempted to explore and compare the myriad design configurations that are possible in that space. Besides this, few studies have been able to deliver a comprehensive understanding on how certain parameters, intrinsic and extrinsic to the FOHWWEC system, influence its performance. The present study is the start of that space exploration and understanding. Three FOHWWEC design configurations (DC), based on the substructure stability principle, are proposed. Vertical cylinders are used as substructure and two spherical point absorbers are connected through a PTO without mechanical spring to the cylinder supporting the WT. The objective is to compare their performances, based on two variables: the annual average absorption width and the maximum standard deviation of the horizontal nacelle acceleration. Besides this, three draft levels are considered and their impact in the performance is also analyzed. The hydrodynamic analysis of the FOHWWEC with parked WT is performed in the frequency domain. Hydrodynamic coefficients and wave-excitation forces are obtained from the BEM solver NEMOH. The software FOHWWEC Analysis program, developed by the author, solves the EoMs and calculates the performance variables. The North Sea is the selected region and a JONSWAP spectrum has been applied. The results indicate that the design configuration 3 (DC3) FOHWWECs have a wave power absorption mechanism based on the heave resonance of both, substructure and WECs. This mechanism is more efficient than DC1 and DC2's mechanisms. This allows to maximize the absorption width. Besides this, DC3 FOHWWECs can also minimize the nacelle accelerations (DC3-D2 case). The effect of the draft on both performance variables differs depending on the DC. Wide-ranging deductions from the results can be summarized as follows. It is reasonable to design a FOHWWEC as a whole system, considering both, wind and wave power generation from the beginning. Using an existing substructure means to lose performance improvement opportunities. It is also reasonable to select a buoyancy-stabilized substructure for the design. This allows to reach the most efficient wave power absorption mechanism, while providing the required flexibility to thoroughly explore and find the balance between design parameters such as WPA, displacement, draft, size and position of the WECs, mooring, among others.