Body ownership (the feeling that one's body belongs to oneself) is commonly studied with Rubber hand illusion (RHI) paradigm that allows inducing a temporary illusory feeling of ownership of a life-sized rubber hand. However, it remains unclear whether illusory ownership of the fake hand relies on the same mechanisms as ownership of one's own real hand. Here, we directly compared ownership of the own hand (OH) and fake hand (FH) in the same set of conditions within immersive virtual reality. We obtained behavioral (proprioceptive drift) and subjective (questionnaire) measures of ownership and disownership for virtual OH, FH and object (Obj) that were located congruently or incongruently with the participant's real hand and were stimulated synchronously or asynchronously with the real hand. Both OH and FH (but not Obj) were embodied after synchronous stimulation in both locations. Crucially, subjective ownership of the OH was stronger than of the FH in congruent location after synchronous stimulation. It was also present after asynchronous stimulation, being stronger when the virtual OH was subjectively more similar to the real hand. The results suggest that the detailed appearance of the body might act as an additional component in the construction of body ownership.