I'm a repeat offender for not providing closure to the threads I start. So I'll at least try this time round.
First off, some facts.
14" 10 hole 2.3 flanged hoop: 650g
14" 10 hole S-hoop: 725g
14" 10 hole Yamaha die cast aluminium hoop: 405g
Now, to my initial question.
Comparing the S-hoop is rather straight forward. As far as I can tell, it's essentially a flanged hoop but with added mass and a particular design. This tends to diminish the high end a bit and render the snare darker sounding and, to my ears, a tad more woody but not necessarily rounder. However, the essential character of a regular flanged hoop is still there, it just seems a little "EQ-ed".
The Yamaha aluminium die cast hoop on the other hand is quite unique. While it sounds more controlled than regular flanged or S-Hoops, it also has an open sounding, almost breathy quality compared to the "boxy" or "dampened" or even "choked" sound that is sometimes associated with zinc die-cast. I noticed some of those attributes on a Sonor Delite snare with very heavy cast hoops (over 1000g per hoop). A very nice sounding drum but the heavy cast hoops just seemed to suppress too much of the qualities of the shell. Not choked, but just too contained. Also, rim shots on those hoops were piercing, as in harsh. Rim shots on the aluminium hoops are easier on the ears (and wrists) while still resulting in a good crack. With heavy cast hoops, the centre of the head always seems to feel quite hard, even on medium tuning. Again, the aluminium hoops alleviate this problem.
Now, the above only corroborates what others have already known or suspected. However, I think there's a very fundamental aspect of the aluminium hoops that hasn't been stated .
With flanged hoops (regular and S-hoop), and to a degree even with zinc die cast hoops, I find that there's a certain metallic quality/character added to a drum. There is a lot less of this metallic quality with the aluminium die cast hoops, especially when used on drums with wood shells. Knowing that many drummers go for wood snares for the tone and warmth of the shell, I've been amazed at how the hoops can alter/impact those qualities. The aluminium cast hoops make my maple snare sound so much rounder, warmer, and with a fuller, woody tone. Well what d'ya know, a wood snare that sounds woody and round, like it actually is!
To resume, I think the S-Hoop is closely related to the regular flanged hoop, but the aluminium die cast hoop should be put in another context. Rather than simply placing it soundwise between a flanged and a zinc die cast hoop, I would say that it's perhaps in between those two and wood hoops (although I have no experience of wood hoops). In any case, the aluminium hoops have a rare capacity to let the tone of the shell really come to the fore.