Sound event recognition systems are rapidly becoming part of our life, since they can be profitably used in several vertical markets, ranging from audio security applications to scene classification and multi-modal analysis in social robotics. In the last years, a not negligible part of the scientific community started to apply Convolutional Neural Networks (CNNs) to image-based representations of the audio stream, due to their successful adoption in almost all the computer vision tasks. In this paper, we carry out a detailed benchmark of various widely used CNN architectures and visual representations on a popular dataset, namely the MIVIA Audio Events database. Our analysis is aimed at understanding how these factors affect the sound event recognition performance with a particular focus on the false positive rate, very relevant in audio surveillance solutions. In fact, although most of the proposed solutions achieve a high recognition rate, the capability of distinguishing the events-of-interest from the background is often not yet sufficient for real systems, and prevent its usage in real applications. Our comprehensive experimental analysis investigates this aspect and allows to identify useful design guidelines for increasing the specificity of sound event recognition systems.