Does it feel the same when you touch an object in Augmented Reality (AR) or in Virtual Reality (VR)? In this paper we study and compare the haptic perception of stiffness of a virtual object in two situations: (1) a purely virtual environment versus (2) a real and augmented environment. We have designed an experimental setup based on a Microsoft HoloLens and a haptic force-feedback device, enabling to press a virtual piston, and compare its stiffness successively in either Augmented Reality (the virtual piston is surrounded by several real objects all located inside a cardboard box) or in Virtual Reality (the same virtual piston is displayed in a fully virtual scene composed of the same other objects). We have conducted a psychophysical experiment with 12 participants. Our results show a surprising bias in perception between the two conditions. The virtual piston is on average perceived stiffer in the VR condition compared to the AR condition. For instance, when the piston had the same stiffness in AR and VR, participants would select the VR piston as the stiffer one in 60% of cases. This suggests a psychological effect as if objects in AR would feel " softer " than in pure VR. Taken together, our results open new perspectives on perception in AR versus VR, and pave the way to future studies aiming at characterizing potential perceptual biases.