Compression of optical field data is of interest due to the many applications where this kind of information processing is necessary. In particular, holographic recording has significant requirements in a high volume of both phase and amplitude data. We analyze and present a comparison between the performances of two lossy compression methods applied over optical field data: the optical scaling compression technique based on a virtual optical system that performs a scaling of the optical field data, and the JPEG format. In particular, we study the compression of optical fields data extracted from off-axis digital holograms. Our results show that optical scaling is better suited for the compression of the highly random phase information found in the optical field data of 3D diffuse objects. Data loss and volume reduction for each method are measured and compared.