Okay, Mark, here it is.
The Supreme is a "lowboy" version of the world-famous Ultramax. The Ultramax is a one-piece toilet with an excellent flush. One-piece means that the tank and toilet are molded as one unit, rather than having a separate tank and bowl.
The lower height of the "tank" part of the one-piece Supreme toilet means that the flush has a little less oomph, but not by much. And in a NYC apartment, it's a nice low flat-ish (not flat) surface to pile stuff on!!
The Eco-Supreme is the 1.28 gallon-per-flush version of the original Supreme, which had a GMax flush. This was Toto's first, famous, effective flush. The design of the trapway, along with the siphon jet at the bottom of the bowl, sucks a lot of waste out of the bowl with very little water. The 1.28 and 1.6 gallon-per-flush are essentially equally as effective these days; the 1.6 version has a bowl that holds a little more water for...um...covering stuff up (the "water spot" is larger, in other words, but not by much). The GMax/EMax Supreme is a very good toilet. The only beef people have, if it's a beef, is that because Toto focused on having a great flush, there is a little less bowl wash than their newer versions.
The Supreme II is a version of the Supreme that uses the Double-Cyclone flush. The trapway and siphon jet design are similar, so the flush is effective, but in the Double-Cyclone, Toto sends the bowl-rinse water out of two horizontal jets at the top of the bowl (rather than through little downward-facing pinholes at the top of the bowl). The water swirls around ("cyclone") the bowl before going out the bottom, giving a little better bowl wash than the EMax.
The Supreme is a regular height bowl. The Supreme II and the Carolina II are "comfort height" bowls: a little taller, which is easier on the knees of a lot of people.
Finally, the Carolina II is a "skirted" version of the Supreme II. It accommodates Toto's Unifit Adapter, which can be had in 10" and 14" versions as well as the 12" version that it comes with. This lets you get the same distance from the wall for the toilet, regardless of whether the toilet flange centerline is placed at a standard 12" or the less-common 10" or 14" distance from the finished wall. The "skirted" toilet also hides the outline of the trapway and some find it easier to clean.
We have both types and I am indifferent between the two. We got the skirted because we had a 10" rough-in, and the toilet (a Carlyle II, skirted version of the Ultramax II) works very well. I also have both double-cyclone and G-Max flushes at home, and the Double-Cyclone is cool and performs as advertised, but the basic GMax works perfectly well.
The Supreme II and the Carolina II also come with CEFIONTECT as standard equipment. This is a nanotechnology-designed coating that makes the rinse a little more effective; stuff doesn't stick to it as much.
So there ya go!