The direct detection of exoplanets has been the subject of intensive research in the recent years. Data obtained with future high-contrast imaging instruments optimized for giant planets direct detection are strongly limited by the speckle noise. Specific observing strategies and data analysis methods, such as angular and spectral differential imaging, are required to attenuate the noise level and possibly detect the faint planet flux. Even though these methods are very efficient at suppressing the speckles, the photometry of the faint planets is dominated by the speckle residuals. The determination of the effective temperature and surface gravity of the detected planets from photometric measurements in different bands is then limited by the photometric error on the planet flux. In this work we investigate this photometric error and the consequences on the determination of the physical parameters of the detected planets. We perform detailed end-to-end simulation with the CAOS-based Software Package for SPHERE to obtain realistic data representing typical observing sequences in Y, J, H and Ks bands with a high contrast imager. The simulated data are used to measure the photometric accuracy as a function of contrast for planets detected with angular and spectral+angular differential methods. We apply this empirical accuracy to study the characterization capabilities of a high-contrast differential imager. We show that the expected photometric performances will allow the detection and characterization of exoplanets down to the Jupiter mass at angular separations of 1.0" and 0.2" respectively around high mass and low mass stars with 2 observations in different filter pairs. We also show that the determination of the planets physical parameters from photometric measurements in different filter pairs is essentialy limited by the error on the determination of the surface gravity.