The old SPSS manual (Nie, Hull et al) maintaned that Kendall's tau-b was
superior to Spearman's rho when there were many ties or a small number
of individual values in one of the variables. I am not sure of the
evidence for this - does anyone know?
>>> Is the spearman test run in stata corrected for ties?
In -spearman- the correlation is just the Pearson correlation
calculated on the ranks. Thus Stata does nothing special about
ties. I think Stata here shares in a widespread prejudice: if
ties are an issue for you, then either your sample is too small
or the data are too problematic for Spearman to be appropriate.
Getting the P-value exactly right if the main idea is dubious
is putting the emphasis in the wrong place. No doubt other
software can fill the gap.