Struggle for Mastery unfortunately does not have any footnotes, and the bibliography at the end doesn’t really help explain where he got these numbers from, but nevertheless David Carpenter is about as trustworthy as an historian could be and I don’t doubt him. Elsewhere (in The Minority of Henry III), Carpenter says the revenues from Aquitaine are discussed in John Gillingham’s book The Angevin Empire, which is also an excellent source, so here is what Gillingham says about it:

Up until 1204, Normandy and England were basically one and the same for administrative purposes, so revenues from Normandy are included in all the vast amounts of financial records produced by the English exchequer. The other Angevin territories weren’t integrated into English administration like that, so we simply don’t know what the revenues were from Anjou, Poitou, Aquitaine, etc.

“The hardest problem of all is to estimate the revenues of Anjou and Aquitaine. No financial accounts survive from the Angevin period but it does not follow from this that the revenues were insignificant. They are unknown and we must make a judgement as to whether we think them large or small.” (Gillingham, pg. 60)

Like you, Gillingham says that just from looking at the map, logically Aquitaine should have produced an enormous amount of revenue. He quotes the English chronicler Ralph Diceto, who wrote:

"Aquitaine overflows with riches of many kinds, excelling other parts of the western world to such an extent that historians consider it to be one of the most fortunate and flourishing of the provinces of Gaul. Its fields are fertile, its vineyards productive and its forests teem with wild life. From the Pyrenees northwards the whole countryside is irrigated by the River Garonne and other streams..." (Quoted in Gillingham, pg. 61)

There are no financial records at all for Angevin Aquitaine, and only a couple of later accounts for Anjou and Poitou, from 1221 and 1238 respectively, after they had been conquered by the Capetian kings of France. The Capetians collected about 1500 pounds from Anjou in 1221 and a little less than that from Poitou in 1238. Does that mean that’s how much revenue the Angevin kings of England wold have collected too? Maybe, but it’s also possible that those accounts don’t reflect the situation earlier in 1200, and as Gillingham says

“it would be rash to conclude that the Angevins received only some £3,000 from the whole of Anjou and Aquitaine.” (Gillingham, pg. 97)

It’s also very likely that revenues produced in the mainland Angevin territories stayed there, to help defend against the Capetians. Revenue from Aquitaine may have been spent entirely in Aquitaine and simply wasn’t recorded in England.

So Aquitaine wasn’t actually 24 times poorer, and it actually may have been quite a bit wealthier. The problem is simply that we don't have the financial records for Aquitaine that exist for England and Normandy.

Sources:

David Carpenter, The Struggle For Mastery (Penguin, 2005)

David Carpenter, The Minority of Henry III (University of California Press, 1990)

John Gillingham, The Angevin Empire, 2nd ed. (Oxford University Press, 2000)