That is a nice picture of a Barred Owl. The heavy well-separated streaks on the breast and eye color (dark vs. yellow) are both distinctly different from that of the Great Gray. The markings in the facial disk are also distinctive — e.g. the fine even lines in the Great Gray vs. the blurry, more disordered pattern in the Barred. (Also Great Gray Owls are even bigger: 60-80+ cm long vs. 40-50 cm for Barred Owls.)
An excellent resource for identifying North American birds is the Cornell Lab of Ornithology's All about birds site. That link is to their comparison between these two species.