It's revealed that the Empire was essentially designed to fail. And they did a good job; in that what we are exposed to in StormBlood shows us that the Empire operates its provinces at a economic loss. Extrapolating; we can see that's likely the Empire had no real chance of defeating the Eorzean alliance after the defeat of the 14th legion. Put simply; the reason why the Empire did not mobilize an overwhelming military responce to the Eorzean invasion of Alamigho is because no such force was availabe. The Empire likely expends nearly it's maximum force projection on supressing the near constant insurrections that boil up in nearly every corner of the empire.
Judging also by their apearance and by what we know of their georgraphy, Garleans are a minority in their own empire; and their conscript army of foreign peasents probably stretches the Garlean economy to it's breaking point. Even without the royal family drama in the post ShadowBringer scenes; Garlemald it self would be in constant unrest, and what ever financial infrastructure was set up to support the Empire's expeditionary military would be highly corrupt and constantly on the brink of a great-crash style break down.
A functional eorzean alliance all but insures the Empire would lose the war; and a protracted war with Eorzean Alliance garuntees a loss. Eorzea, on the other hand, showed signs of increasing sophistication and logisitical competence. It is likely that as the war progressed as Eorzea was increasingly able to organize an industrial wartime economy; It is likely that Ishgard and Limsa would come out as the Strongest economies thru and post war. Ishgards growth as an industrial power would see its first major export be Arms and ammo.. to everyone basically; while Limsa is a better positioned logistical hot spot, especially as Trade increases to the far east. In a realist sense where we minimized the main story and focused on this as a World-war Scenario; the Empire would take several years to defeat. But when the lines finally broke, Eorzea would be in Garlemald proper very quickly. The Empire would likely surrender when it became obvious that they could not protect Garlemald it self.
The Post war:
Tho Ul dah fancies it self as the trading capital; it is actually poorly positioned for that. While it is likely to remain a seat of financial power, it's Ishgard that would see the Post-war Boom. Ishgard would be the worlds' largest arms exporter and the most likely place for Garlean technicians and scientists to flee to in the post-war. A explotion in demand for air-ships, the work to refit and recycle imperial military hardware, and the expansion of industrial and than consumer goods that would follow the end of the war would be centered on Ishgard; with Limsa being a close second seeing both a manufacutring boom and a logisitical trade boom oveer land-sea-and-air.
We could expect Girdania to largely reject industrialization; and chose instead to remain relatively static, with some growth perhaps in tourism and education. Ul'dah would likely either become irrelevant over time or position it self as Eorzea's banking and financial center; while Ala mhigo would spend years dependent on the alliances aid and trade. It would likely take decades (3-4) for them to return to Pre-occupation population and economic power. Finally; the east would likely recover easier as more of its infastructure remains intact. Over the following decade, it would modernize, recover and be a large part of the reason why Limsa becomes such a trading power house in the post-war. The Post-Garlean war would bring about the Ishgardian century.