For one thing, the sky looks incredibly different when you look at different frequencies of photons. If you look at visible light, you have the enormous powerhouse of the sun, the band of the galaxy, the Magellanic Clouds, and some very bright stars. If you look at gamma rays, you see an isotropic distribution of point sources. If you look in the far infrared, you see the galaxy, the dipole anisotropy caused by the proper motion of the Earth with respect to the cosmic background radiation, and the cosmic background radiation itself. The x-ray and radio bands show you other things besides.
I would expect that the appearance of the gravitational sky would also be strongly frequency-dependent. Quasars, binary pulsars and galactic clusters would figure prominently, I imagine, as would the rapidly moving stars at the center of our galaxy. The most interesting possibility is that the brightest sources may well be sitting back at the inflationary epoch, far earlier than anything we can see with electromagnetism.