Disks around CQ Tauri and MWC 758:: dense PDR or gas dispersal?

Context. The overall properties of disks surrounding intermediate PMS stars (HAe) are not yet well constrained by current observations. The disk inclination, which significantly affects spectral energy distribution modeling, is often unknown. Aims. We attempted to resolve the disks around CQ Tau and MWC758 to provide accurate constraints on the disk parameters, in particular the temperature and surface density distribution. Methods. We report arcsecond resolution observations of dust and CO line emissions with the IRAM array. We also searched for the HCO+ J = 1 -> 0 transition. The disk properties are derived using a standard disk model. We use the Meudon PDR code to study the chemistry. Results. The two disks share some common properties. The mean CO abundance is low despite disk temperatures above the CO condensation temperature. Furthermore, the CO surface density and dust opacity have different radial dependence. The CQTau disk appears warmer and perhaps less dense than that of MWC 758. Modeling the chemistry, we find that photodissociation of CO is a viable mechanism to explain its low abundance. The photospheric flux is not sufficient for this: a strong UV excess is required. In CQ Tau, the high temperature is consistent with the expectation for a PDR. The PDR model has difficulty explaining the mild temperatures obtained in MWC 758, for which a low gas-to-dust ratio is preferred. A yet, unexplored alternative could be that, despite currently high gas temperatures CO remains trapped in grains, as the models suggest that large grains can be cold enough to prevent thermal desorption of CO. The low inclination of the CQ Tau disk, similar to 30 degrees, challenges previous interpretations given for UX Ori - like luminosity variations of this star. Conclusions. We conclude that CO cannot be used as a simple tracer of gas-to-dust ratio, the CO abundance being affected by photodissociation and grain growth.