Personally, taking it a piece at a time, I like it because...
I like moderate velocity big bores, be it revolvers or semiautos. By "moderate velocity", I mean up to 1000 fps or so. By big bore, I guess anything .40 and up counts, but I think .44 or .45 is the ideal. In revolvers, this is pretty much the .44 Special and the .45 Colt. They are fast enough to do something without being high pressured and stupid loud, and throw bullets big enough to use the velocity they make without beating me to death.
Using an engine analogy, they are big block V8s running at a mid range rpm. A small block (.357) might equal the HP in a smaller package, but it works harder, makes more noise, requires more attention, and puts more stress on things. The big bores/big blocks have the power, but don't strain themselves so much in making it.
Having narrowed it to those two, the 44 spl and 45 Colt...
I like the the .44 Special over the 45 Colt for a few reasons. Most have been listed already.
-It can work in a smaller gun. I have two .44 Spls- a new Ruger FT and a S&W 696- and I consider both to be .357-sized guns. They are just a little smaller than what I consider a typical .44/.45 big bore. I think the .44 SPL is on the edge of being able to manage this, and the .45 Colt can't quite pull it off as it either leaves too little metal in the cylinder or requires a larger cylinder to start with putting us back to a big gun. I have owned a S&W 25-5 (45 Colt) for 25 years and love it, but think it is just a little too big for convenience. Yet I wouldn't want a smaller cylinder in a .45 Colt.
-The .44 bore offers more "revolver-ish" bullet choices. The .45 caliber allows plenty of bullets, but a lot of them are meant for the 45 ACP. Many of those will work in a revolver, but some work bettter than others. With a .44, almost all bullets were designed from the start for revolver use, and there are a lot of 'em.
Of course, for most of us one or two bullets do almost everything we need and they can be found for either. But it's nice to have plenty of choices.
-The dimensions seem to run more consistent. The .45 Colt's various bore and cylinder dimensions over the years have lead to trouble. Some 45 Colts come with cylinder throats smaller than the bore and need corrected (although this seems to be a LOT better anymore). My S&W needed a little attention, but was not near as bad as some I've heard of. I seldom even hear of this with .44s.
-The case has a smaller capacity. Both the 44 Spl and 45 Colt have big cases for what they do. You don't use much of the case capacity with smokeless powder and have empty space in both. With the .44 Special, you have less of it. It's a small difference that won't matter to most people, but it is a difference and matters to me. [/i]