Ka band frequencies are higher than than Ku band. That makes it easier to get higher bandwidth in the key rf components of the system: antenna, amplifiers, converters and filters. Ground antennas can be smaller and that is also a plus. The penalty: probable higher atmospheric attenuation. And getting transmit power on the satellite will be harder but apparently DirecTV thinks they can handle that problem.
Aren't you forgetting about the dipole factor? I mean, of course the dB gain could be the same with a smaller dish. But the actual signal strength, measured as microvolts across the terminals of the dipole, would vary inversely as a function of wavelength.