Found this while looking into a similar thing myself so here's my solution in case it's useful for anyone else...
Note: Harmonic's answer works, depending on scenario though it may be easier to do this instead:
$count = get_category($category->term_id)->category_count;
$category is your taxonomy object.
Important note here being that this assumes no other post_type uses the same taxonomy.
get_category() is actually a wrapper function of
In this case, get_term() has a name__like parameter that get_category() doesn't. There are probably other little differences too.