When the lumped source has size << loop size, I would expect the correct pattern. Maybe some HFSS expert can comment on this one. Can you experiment with the width/length ratio of the lumped source?
Regarding a physical loop, the loop is tuned with a capacitor. As long as there is no large capacitive gap, the loop can be treated as a loop having constant electrical current distribution along the loop. This will result in the pattern you expect.
When the capacitive gap is large, the current segment opposite to the capacitive gap is no longer cancelled (as the displacement current does not radiate). In that case you will get a combined pattern of a Hertzian dipole and that of a loop.