While the "circle notation" for benzene is popular in high school teaching, I have never seen a higher-level organic chemistry textbook that uses it, or met a practicing chemist who uses it. The "Kekule notation" seems to be much more popular among chemists. It is overwhelmingly used in all the major chemistry journals I know, whether published by the ACS, the RCS, Elsevier, or Wiley. In my opinion, the reason is that once you go beyond benzene and start to look at heterocycles, polycyclic aromatic molecules, reactive intermediates, and reaction mechanisms, the Kekule notation makes electron counting and "electron pushing" much more straightforward. The circle notation only seems to be common for some organometallic compounds such as ferrocene and some aromatic ions such as the cyclopentadienyl anion and the tropylium cation.