Conductive hydrogels are of interest for highly flexible sensor elements. We compare conductive hydrogels and hydrogel foams in view of strain-sensing applications. Polyvinyl alcool (PVA) and poly(3,4-ethylenedioxythiophene (PEDOT:PSS) are used for the formulation of conductive hydrogels. For hydrogel foaming, we have investigated the influence of dodecylbenzenesulfonate (DBSA) as foaming agent, as well as the influence of air incorporation at various mixing speeds. We showed that DBSA acting as a surfactant, already at a concentration of 1.12wt%, efficiently stabilizes air bubbles, allowing for the formulation of conductive PVA and PVA/PEDOT:PSS hydrogel foams with low density (<400 kg/m3) and high water uptake capacity (swelling ratio > 1500%). The resulting Young moduli depend on the air-bubble incorporation from mixing, and are affected by freeze-drying/rehydration. Using dielectric broadband spectroscopy under mechanical load, we demonstrate that PVA/PEDOT:PSS hydrogel foams exhibit a significant decrease in conductivity under mechanical compression, compared to dense hydrogels. The frequency-dependent conductivity of the hydrogels exhibits two plateaus, one in the low frequency range, and one in the high frequency range. We find that the conductivity of the PVA/PEDOT:PSS hydrogels decreases linearly as a function of pressure in each of the frequency regions, which makes the hydrogel foams highly interesting in view of compressive strain-sensing applications.