Sorry for the long response time, here, as I ha dto go diggin' through original documentation rather than the Wiki. The GDP numbers are extrapolated from the "Wealth per capita" figures rather than being concrete. The average UCAS citizen brings in around 28,000Y a year, while the average CAS citizen brings in around 25,000Y a year. The cost of living is about 75% of the UCAS rate, but high tech is more expensive, which is about right. In essence, you can live dirt-cheap in the CAS, but you can't get the cutting edge stuff as easily, which is pretty much the same as today.
UCAS has around 170 million people, CAS around 110 million, while Aztlan has around 135 million. We don't know if this number includes corporate citizens, but we'll assume it does for all three to make life easy.
In terms of magical strength, we know that the CAS and the UCAS have a general parity, despite the much smaller CAS population. It's safe to assume that Aztlan was much stronger in the time of Darke and the plotlines where they tapped Horrors and the Blood Gestalt, but that whole group got waxed, the plot killed, and the manaspike closed off. How powerful they are now is a matter of opinion, but I'd say it's safe to say lower than before, but likely a tad stronger than the UCAS or CAS, which are more mundane nations. (The UCAS more than CAS, as shown above.)
In military terms, Aztlan only has about 30,000 combat forces, mostly in the army, but also has around a hundred thousand Aztechnology soldiers to draw from. They have a strong army, a middlin' air force, and no appreciable navy. Aztechnology doesn't have much of a navy either (A few escorts for anti-piracy work, but no main battle craft, aircraft carriers, etc) nor a large air force. Aztlan's forces are intended for protection, not force-projection, so they have no long-range bombers, but do have old-school tube-based artillery. This proved quite effective against the Texas National Guard when they last met. It's reasonable to assume that they have rings of guns set up akin to North Korea of today, keeping an eye on Texas cities, but to a far smaller degree. Aztlan and Aztechnology forces are split among the border with PCC, CAS, the Yucatan, and Amazonia, while the navy largely deals with carribean pirates. The western Azzie navy hangs out in San Deigo, but doesn't seem to do much.
CAS has around 90,000 in the army, an air force (but no official numbers are given), and a surprisingly strong navy. There are two carrier groups (But these are smaller, 35,000 ton carriers, not the supercarriers of today), a large number of brown-water ships, and the largest submarine force on the planet. Initial reports were that they had no boomers (nuclear-equiped subs) but this has since been revealed as false as the mothballed units that they had were trotted back out when border tensions grew too hot. (Of course, they won't use said nuclear devices, rendering them a moot point, but.) ... the CAS also has a unique unit in the world in that they have submersible mini-carriers, each holding about a wing (6 planes) of manned, or unmanned, aircraft. It's unknown how many of these that they might have. (At least one, probably a few, but not lots.)
CAS forces are well-trained, better than the average military, but aren't as well-equipped. CAS special forces are minimal, certainly no match for Souix WIldcats. Hazarding a GUESS, I'd put them on par with Leopard Guards, but not as skilled as Eagle or Jaguar.
The CAS airforce is higher tech than Aztlan's, but nowhere near as advanced as the PCC. CAS does have long-range strategic bombers but, due to their isolationist stance, they likely lack any sort of refueling force to allow a true worldwide range.
The CAS has friendly borders with the UCAS, keeping mainly anti-dmuggling border patrols rather than combat troops in these areas and the PCC. Relations with the Carribean fluxuates, but they have no military to speak of, so CAS forces here are just anti-pirate in nature and a token military presence along Florida's border. The bulk of CAS forces are in Texas, along the Aztlan border... in return, Aztlan keeps over 30,000 men on their side of the border, but most of these are Aztechnology assets rather than national units.
Overall, Aztlan is a more powerful nation than the CAS once Aztechnology forces are brought into the math, but suffers from having a hot border, a recently-hot but starting to cool border, and two unfriendly borders, with the hotter borders a huge distance away from the cooler, while CAS has only one unfriendly border, allowing a greater spearhead strength. Aztlan has better special forces but poor ability to infiltrate them, while CAS has good infiltration methods but average special forces who might be routed out before being able to cause any harm. The CAS airforce has better striking ability than the Azzie, but not as much durability ... over time, Aztechnology reliability will take over as CAS air assets are more and more under the wrench, but, initially, they have the advantage. There's certainly a race to see if the CAS air power can take out Aztlan's entrenched artillery units before they can unleash doom across the TExas-Azlan border. This "I might go down, but I'll take you with me!" murder-suicide pact is probably a big reason why the CAS has never gone in to try and retake the land... see also: North Korea holding Seoul hostage. CAS special forces being generally weaker than Aztechnology's means the slipping in to take these units out beforehand is also a very unlikely event.
Oh, and we know that during the Yucatan war, and later Amazonia's war, the Azzies reduced the CAS borders to a skeleton crew, which lead many Southern generals to chomp at the bits for a "Now is the time!" moment, but they didn't pull the trigger. Thanks to Los Angeles and Ghostwalker's kicking them out of Denver, the Azzies have also moved troops less to the CAS border than to the PCC one, looking hungrily as LA and Denver. This has caused the PCC to get much cozier with the CAS than ever before, and a mutal defense policy seems likely, if as-yet unmentioned in any source material. The PCC, of course, has a smaller military but a vastly more high-tech one, the strongest air force in the Americas, and brutal, brutal level computer assets that neither Azlan or CAS can match. It's assumed that they have some Wildcats on-call, but their own special forces are about average or just below.
So, overall, I give the edge to CAS, who have greater first-strike ability and a more focused force, who also have the naval assets to attack from the flanks, but it'd be ugly and Texas would get creamed in return. The Azzie forces are just split along too many fronts just now and could be pushed back on one if pushed hard enough. With the CAS border being the coolest of the four (discounting the Carribean, natch), it's the least likely to see elite units stationed there, which were used in the Yucatan and now are split between the Amazon (most) and the PCC (the minority). Then again, the Azzies have combat-tested troops while the CAS forces haven't seen actual combat (other than minor border exchanges) in a generation. Seasoned command personell can't be underestimated and I'd wager that, while the initial Aztlan forces would fall back quickly, the command staff would be able to soften the blow and establish very effective counter-punches, not to mention insurgency that would break out, backed by Jaguars.
Phew!
That's a lot of yammering!
