While in both cases the growth of the profession started at similar times, doctors seem to have doubled while lawyers quadrupled in the same timeframe.
EDIT: I just remembered that I think this is mentioned in The Rise and Fall of American Growth and that it was attributed to an increase in specialization
wikipedia shows the same rise of doctor per capita that look suspiciously the same as the lawyer rise:
https://en.wikipedia.org/wiki/File:Physicians_in_the_United_States_per_10,000_people_(1850-2009).svg
While in both cases the growth of the profession started at similar times, doctors seem to have doubled while lawyers quadrupled in the same timeframe.
Hm. Very interesting.
EDIT: I just remembered that I think this is mentioned in The Rise and Fall of American Growth and that it was attributed to an increase in specialization