There is no straightforward, simple answer to this.
Here are some thoughts from me and some of my colleagues:
 
These conical sections are usually called "swaged sections." A general literature search yielded very little. A search of the FRI electronic files yielded nothing.
 
This is a mechanical design issue that depends on shell pressure, shell thickness, upper diameter and lower diameter -- hence there are no universally applicable rules of thumb.

Some people say that a diameter change of less than 1.5 feet is never worth it. Some say that the minimum vertical distance of the swaged section should be 36 inches. Some say that the angle of the swaged section should be a maximum of 30 degrees from vertical (therefore the cone should be more vertical than horizontal  --  for mechanical strength).
 
Some people claim that dual-diameter columns usually have a larger lower diameter. This is not really true -- many columns have larger upper diameters.
 
The FRI Column has an 8-foot diameter upper section and a 4-foot diameter lower section.
The angle is 25 degrees from vertical.
The swaged section is 4 feet tall (vertical measurement).
 
Ultimately, a mechanical engineer needs to perform calculations and decide.