Unfortunately we don't have the numbers built for the Monsoon and Farragut to be able to declare one as a flagship and the other the main line unit.
Personally, I see the Farragut as just a technological improvement over the Monsoon, with design features refined by the HAF's experiences in the Age of War. The Monsoon was a peacetime design, with the first built 30 years before the beginning of the Age of War, while the Farragut incorporates 50 years of actual combat experience. The Farragut is a much toothier design, with less of a cargo tail, and even has fewer docking collars, keeping costs low (the Farragut is less than a billion C-Bills more expensive than the Monsoon, despite being so much superior in all bar dropship capacity) and thus reducing the financial impact if lost in battle.
The Texas is the product of the later SLDF's requirements and thus is again a peacetime design. It reverts to the 6-collar, large cargo bay theme of the Monsoon, with a similar relatively modest armament, providing much less raw firepower than the wartime Farragut. There is still technological improvement and the Texas was built to be the most survivable WarShip to date, but it's definitely a product of the SLDF's desire for transportation over combat capability, even allowing a reduction in size compared to the Farragut.
The McKenna is something of a combination of the two themes, spurred by an otherwise unexplained doctrinal change mentioned in the Farragut's fluff: it takes the transportation capability of the Monsoon and Texas and the heavier armament of the Farragut, with the latter enhanced by the bracketing capability seen on the Texas. The need to combine both makes the McKenna much bigger than the preceding battleship classes, which together with the addition of the LF battery makes it massively more expensive too, coming out at nearly double the price of the Texas.
Cost obviously wasn't a concern for the SLDF and they equally obviously preferred the McKenna, hence why they built so many more compared to the slightly older Texas. While this could perhaps be seen as proof of a flagship/ship-of-the-line split, with fewer command vessels needed than the frontline killers, the very fact that the Texas lacks a LF battery argues against that. Quite simply, the Texas was built in fewer numbers because, while usable enough to keep in service, it was less capable than the McKenna.