  We present deep, high-quality K-band images of complete subsamples of
powerful radio and sub-mm galaxies at z=2. The data were obtained in the best
available seeing at UKIRT and Gemini North, with integration times scaled to
ensure that comparable rest-frame surface brightness levels are reached for all
galaxies. We fit two-dimensional axi-symmetric galaxy models to determine
galaxy morphologies at rest-frame optical wavelengths > 4000A, varying
luminosity, axial ratio, half-light radius, and Sersic index. We find that,
while some images show evidence of galaxy interactions, >95% of the rest-frame
optical light in all galaxies is well-described by these simple models. We also
find a clear difference in morphology between these two classes of galaxy; fits
to the individual images and image stacks reveal that the radio galaxies are
moderately large (<r{1/2}>=8.4+-1.1kpc; median r{1/2}=7.8), de Vaucouleurs
spheroids (<n> = 4.07+-0.27; median n=3.87), while the sub-mm galaxies appear
to be moderately compact (<r{1/2}>=3.4+-0.3kpc; median r{1/2}=3.1kpc)
exponential discs (<n>=1.44+-0.16; median n=1.08). We show that the z=2 radio
galaxies display a well-defined Kormendy relation but that, while larger than
other recently-studied high-z massive galaxy populations, they are still ~1.5
times smaller than their local counterparts. The scalelengths of the starlight
in the sub-mm galaxies are comparable to those reported for the molecular gas.
Their sizes are also similar to those of comparably massive quiescent galaxies
at z>1.5. In terms of stellar mass surface density, the majority of the radio
galaxies lie within the locus defined by local ellipticals. In contrast, while
best modelled as discs, most of the sub-mm galaxies have higher stellar mass
densities than local galaxies, and appear destined to evolve into present-day
massive ellipticals.
