“What’s the functional difference between front loaded and horn loaded speaker cabinets and why would I use one over the other?”
Horn loading is actually a very complicated issue that even after decades of research is still being perfected. A lot of this research has been focused on working with compression drivers to control their coupling with the air. It sounds, however, like your question is more directed towards speaker cabinets as opposed to what we more normally think of as horns and tweeters. While all of the same complex issues apply in speaker cabinets there are some different techniques that can be employed due to the normal range of frequencies involved and the drivers used to reproduce them.
In a VERY general sense you can sum it up as follows: Horn loaded speakers will tend to be louder than their front-loaded counterparts, and will be more directional. The additional loudness often amounts to somewhere around 3dB (though it can be less than that) and comes primarily from focusing sound that would have otherwise spread out in a much wider pattern of coverage than what the horn dictates (this, of course, also varies by wavelength as well as the shape and size of the horn).
Historically horn loaded enclosures have been used in large venues for two reasons related to the differences outlined above: 1) They can more easily reach a desired SPL with less amplifier power than front loaded designs, and 2) Because the dispersion is more controlled due to the horn it can be easier to get better behavior from multiple cabinets interacting and interfering with one another. This is another rather complex issue, but suffice to say that all kinds of strange things happen when multiple drivers cover the same physical area with the same frequency range of sound. You will always get an effect known as lobing, where certain frequencies will have hot spots and other frequencies will have dead spots. (Something designers of many guitar and bass cabinets use to their advantage.) In a PA system it’s really can be a mess, and quite often inexperienced engineers seriously compromise a perfectly good sounding system by combining speakers in a haphazard way. One remedy for this is horn loaded enclosures that control the dispersion of the speakers in such a way that they don’t overlap as much. (There is also a newer technique of scientifically predicting these interactions (with computer models) and taking advantage of them in the design. While that isn’t particularly relevant to this discussion it does make using front loaded arrays much more feasible.) The tighter dispersion and greater SPL of horn loaded designs also tend to result in a cabinet that can throw sound a greater distance, which is where you hear the term “long-throw” come in to play a lot.
Those factors are all well documented. What you will not read as much about is the subjective sound quality differences many engineers observe between the two designs. Ideally there wouldn’t be much difference; the idea being that the cabinet should simply reproduce reality regardless of the basic design philosophy. After wiping the collective smirks off our faces for that statement we can now return to the real world and consider that front loaded designs really can sometimes sound different from horn loaded designs. The difference can subjectively be characterized by thinking of how a voice sounds when coming through a horn, like a bullhorn or something. There is sometimes a certain nasal quality that gets accentuated, although in a properly designed cabinet it is much less noticeable than the aforementioned bullhorn. In fact, in modern designs these problems are all but eliminated. Even in cabinets where the phenomenon does exist do not assume that the cabinet is ‘bad’ and will not sound good. In many applications the control over the dispersion actually results in better sound once you are out in the room environment listening to the overall result.
The really good news is that we hardly have to worry about this type of stuff these days. Most cabinets are much more carefully designed than they were even a few years ago, and with very few exceptions they all sound remarkably good. Horn loaded designs will still, all other things being equal, throw sound further, and generally with a tighter pattern of coverage (which could be good or bad depending upon your circumstances), but the sound is all so good these days you can really focus on your mix and the overall settings of the PA a lot more.
(Back when your inSync editor was young we usually built all our own speaker cabinets because we had no money. Talk about crappy sound. We didn’t know better, but we learned a lot along the way.)