If the left branch is the one where the current local HEAD is, then you might try to invoke that gitk log
with the"right" branch checked out first (I realize it is a -- poor -- workaround, but my point is: gitk
won't do it for you).
However, as far as I know, gitk
won't display one branch rather than the other or detect the "busiest" one. Only log options can influence how the history of commits is represented (as in "Visualizing branch topology in git").