Fatal error: Class 'DrupalDefaultEntityController' not found in comment.module
After a bit of research, I found out that the problem might be generated from entity.inc inside the includes folder. 
Therefore, I tried to put back the previous entity.inc (from the 7.65 installation); subsequently, I run the update.php script, and after another refresh, the website is finally accessible. 
I done few more tests to check if there are warnings or errors, but everything seems to work fine, so somehow I got it sorted.