The perception of size in virtual objects in Augmented Reality (AR) and Virtual Reality (VR) is a not trivial issue, as the effectiveness of manipulating and interacting with virtual content depends on the accuracy of size perception. However, there are missing straightforward comparisons between VR and AR in terms of size perception for the deep understanding of size perceptual differences. Understanding these perceptual differences can inform designers on how to adapt content when transitioning between these two spatial computing platforms. In this paper, we conducted two psychophysical experiments to measure the perceptual thresholds of size discrimination for virtual objects. Our results indicated that users are more sensitive to size changes in VR than in video see-through AR, suggesting that size differences are easier to be perceived in VR than in AR. Additionally, for increase or decrease of sizes, the accuracy of judgments showed an asymmetric trend in video see-through AR.