actually in general there are 3 different gibson necks on LP standards.
50s, 59 rounded, and 60s slim taper.
50s is obviously thicker, and the 59 being obviously more rounded.
the 60s slim taper, while not exactly 'slim', is as its name implies.
it maintains very even taper/thickness from 1st to 12th fret, whereas the 50s style gets thicker the higher you go up the fretboard.
these are Gibson's own general measurements for the 50s and 60s.
50s.
0.818" (20.8mm) 0.963" (24.5mm)
60s.
0.800" (20.3mm) 0.875" (22.2mm)
to loosely quote gibson on the 60s slim taper, it only increases in thickness less than 1/10th of an inch from 1st to 12th.
i find 50s neck to be much better for LP standards.
just gives the LP more balls, also partly due to the neck having more mass.
60s necks fit SGs more, only exception being the current SG standard whose neck is pretty thick.