Hi, I'm a first time poster. And, for the record, I'm a male teenager with ADD.
I find this discussion slightly odd, because the majority of the TBSes forwarded are FF style JRPGs and Civilization. I don't think this represents the scope of the field. What ever happened to games like X-com, Nethack, Master of Magic, or Galactic Civilizations? The field can't be accurately summed up and analysed by "line-and-fire" style RPGs or one specific strategy game.
I'm more of a TBS gamer over RTS. The only real RTS strategy game I liked was TA Spring (the original TA had waaaay too many bugs to be a classic game). On the other hand, I find video-game RPGs in general boring, Chrono Trigger and Nethack excepting. Allow me to ignore that group; I don't have much experience with them.
The big thing I like about TBS strategy games is the potential complexity they have. RTSes simply cannot have the same sprawling maps or massive armies a game like Master of Magic can have (Spring excepting), nor can they have reach the sheer amount of options Dominions 3 or Space Empires has.
Take Starcraft, for example. I know this might not be the best game to use, but it's one of the RTS I've played the most and still, AFAIK, the most popular one. For small-to-midsize battles, there's a lot of options available. It still does not reach the possibilities most TBS offer. When it comes to larger wars, however, the game is mostly restricted to "make a lot of units." On the other hand, look at what Space Empires 5 offers. In addition to creating superfleets, there's a host of other useful tactics, mostly various things stellar manipulation offers. For example, you can turn systems into black holes or warp smaller killfleets directly into enemy lines, or use a combined virus/espionage/boarders attack to take over large sections of the enemy fleet. Or look at Masters of Magic or Dominions 3. In addition to using armies, you can throw around world-shattering magic to do anything from open portals to hell to call armies of dragons or (in one fun MoM spell) make every single unit that dies rise as a zombie under your control.
I'm not saying that's for everyone. It's scientifically shown that people feel less confident with more options available, and gaining a good understanding of what you can do takes a lot of time and planning. RTSes can offer plenty of tactical complexity without requiring so much time to grasp. They also take less time to play, requiring a few hours as opposed to a few weeks or months. It's more a matter of personal preference than an objective difference.
The other thing I like about TBSes is the time scale. Specifically, things aren't happening really fast. I tend to panic when I have to be in five places at once with a limitted timespan to deal with each. Not only do I do poorly in those situations, but I also have less time to think about my next move or two. With TBSes, though, time is stopped as long as I want it. I have more time to address each issue, and I have time to plan ahead. In my only (there's not enough players

) multiplayer SE 5 game, I spent maybe 20 minutes on each turn. Half of it was analyzing the situation and trying to predict and counter what my opponent was planning, a quarter of it was building and testing new ship designs and fleet tactics, and the rest was actually moving my pieces. Not everybody enjoys that. I do.
Of course, this is also a weakness for the genre. As mentioned before, online TBS games can take weeks or months. They're also completely unplayable if combat isn't somehow automated. This isn't instant gratification or even delayed gratification- it's
belated gratification. It makes it really hard to enjoy games of this type, reducing the number of people who play it. This makes it harder to find online games, making playing online more frustrating and perpetuating a vicious cycle. RTSes aren't nearly as bad in this regard, and generally have more players. Also, since they are take a lot less time to play, you can play multiple RTS games in the time it takes to play one TBS game. This provides a lot more enjoyment and tactical variance if you aren't willing to put up with TBS uber-complexity.
While TBSes are a dying breed, I really wouldn't say they have to remain that way. It's not that hard to produce a TBS, at least not as hard as an RTS. Well over a hundred people worked on Warcraft 3, over twenty of them programmers. Dominions 3 was completely developed by two people, one of them working part-time. Aaron Hall singlehandedly programmed all of the Space Empires games. If people were more willing to buy them, it would be
very easy to oblige.
However, I'd say that many more people lie in the RTS camp than the TBS one. TBSes require a lot of patience and dedication not just to master, but to enjoy. Sure, it gets much easier after learning the first, but the problem still persists. More people are interested in the faster-paced, tactically-acceptable RTS field than the slow-paced, strategically-grandoise TBS field.
I think that sums up most of my major points, those relating to strategy games at least.