I am no expert on welding power supplies, so I am not going to try to explain something I know very little about. I am sure it has something to do with the circuitry of the two types of power supplies. Perhaps the difference is the inclusion of the saturable reactor core in some CC power supply that produces more heat and more power loss as well as the capacitors and other devises used for power factor correction. Take a look at the Welding Handbook on welding processes. They have a pretty good section on power supplies. There are different ways to transform the high voltage, low current supplied by the utilities into low voltage / high current we use for welding.

The equation is taken from the AWS Handbook as well. I find it very useful for sizing power supplies to be used in the field where I have to contend with very long welding leads. The long welding leads translates into voltage losses that have to be taken into account when sizing the power supply. Basically the equation gives you the maximum voltage the power supply can provide when it is under load. The voltage listed, as OCV on the nameplate is the maximum voltage at the terminals when the machine is on, but there is no load, i.e., no one is actually welding. The bottom line is that when you have long welding leads, as is  the case in ship yards or construction sites, there are substantial voltage loses that have to be considered. Therefore the power supply has to have sufficient amperage capacity to provide the voltage required at the welding arc as well as the losses due to the long cables, corroded connections, lose connections, etc.

The information I provided in the previous post was intended to give a person a means of determining the approximate draw at the welding power supply. It does not take into consideration the requirements of the electrical code or the length of the cable from the main circuit breaker box to the welding machine, etc. People always seem to question the information provided by the nameplate on the welding machine. The information on the nameplate is what should be used when determining the actual power requirements of the particular power supply. As you observed, more sophisticated power supplies require more power than a simple power supply that uses a movable secondary core or fixed taps. The saturable reactors produce more heat, which translates into higher amperages for a given input voltage.

The Welding Handbook also mentions that the CC power supplies do require power factor correction due to the inductive reactance.

Best regard - Al