I have to vote for the 60s slim taper neck as found in the classics and some of the custom shops like my Class 5 Les Paul.
The standard neck is much too large for my 5yo sized hands but may thicken the tone somewhat (not that its really a problem with a LP.
"I believe that banking institutions are more dangerous to our liberties than standing armies. If the American people ever allow private banks to control the issue of their currency, first by inflation, then by deflation, the banks and corporations that will grow up around the banks will deprive the people of all property until their children wake-up homeless on the continent their fathers conquered."
-Thomas Jefferson 1802