Square taper uses a 17mm spindle, Octalink and ISIS use 22mm, external bearing (new Shimano) is 24mm (spaced far apart). The spindle stiffness increases exponentially with diameter so Octalink is significantly stiffer than square taper (less chain rub on the front derailleur).

One good thing about square taper is that the spindle is small so there is room for fairly large bearings inside the bottom bracket shell. Some early ISIS bottom bracket’s had problems since the bearings were small but Shimano BB’s have been bullet proof from the start (except for Dura Ace which is not sealed and requires frequent maintenance or the internals will corrode).

In my opinion the new external bearing Shimano cranks are superior to everything else. The spindle is stiffest of the lot, the bearings are spaced wide so they support the spindle well, and the bearings are large for long life. No downside I can think of.