Epoxy resin is widely used in high voltage apparatus as insulation. Fillers are often added to epoxy resin to enhance its mechanical, thermal and chemical properties. The addition of fillers can deteriorate electrical performance. With the new development in nanotechnology, it has been widely anticipated that the combination of nanoparticles with traditional resin systems may create nanocomposite materials with enhanced electrical, thermal and mechanical properties. In the present paper we have carried out a comparative study on dielectric properties, space charge and dielectric breakdown behavior of epoxy resin/nanocomposites with nano-fillers of $SiO_2$ and $Al_2O_3$. The epoxy resin (LY556), commonly used in power apparatus was used to investigate the dielectric behavior of epoxy resin/nanocomposites with different filler concentrations. The epoxy resin/nanocomposite thin film samples were prepared and tests were carried out to measure their dielectric permittivity and tan delta value in a frequency range of 1 Hz - 1 MHz. The space charge behaviors were also observed by using the pulse electroacoustic (PEA) technique. In addition, traditional epoxy resin/microcomposites were also prepared and tested and the test results were compared with those obtained from epoxy resin/nanocomposites.