Okay, my turn to dive into this.
Destroyers and carrier groups are, for all practical purposes, equal in strength and ability to project power. So the question we should be asking is why did the species in FS begin using destroyers and all but abandoned carrier groups? For the Shivans, it's probably a simple issue of "because they can" given their numbers. The Vasudans probably did it because the GTA did it (the Typhon came after the Orion). So why did the GTA do it?
I think it's because the Orion WASN'T designed to replace carrier groups.
Okay, I know that sounds strange, but it makes sense if you think about it. The Galactic Terran Alliance was an originzation tasked with defending the human race and exploration of space. We can assume (reasonably) that the GTA was formed before the Vasudans entered the equation, and if so, then who would the GTA defend against? Pirates, criminals, the occasional errant asteroid, that's about it. So the carrier group makes more sense here as it's more flexible when dealing with this kind of enemy.
Again, reasonably, we can assume that the Orion was built and or designed prior to the discovery of the Vasudans (there is no real canon evidence for this, I might add, but it will seem reasonable in a moment), so why would they build it? Well, the Orion is a very big ship, capable of carrying a lot of supplies for very long duration voyages. It's more than capable of defending itself, has giant hanger bays for fighters and other small craft, and thus it seems to me that it's mission was to explore, the second half of the GTA's mission.
It's your spearhead, a giant ship going out into the unknown, where any number of dangers might exist. Perhaps a new race whom you'll want to impress, or asteroids that cloud the node, or something really unpleasent that wishes to destroy the ship. An Orion is much more capable of protecting itself and surviving a long journey against just about anything than a flimsy carrier and it's battle group in these situations.
The Orion changes from this exploration role to that of a main capital ship simply by the fact that the bulk of the 14 Year War is fought in places far from supply, remote locations that were likely only found because of the war itself (this, btw, is a true statement, most of the war was fought not in Vega and Antares but in the same places as FS2, Epsilon Pegsi, Capella, etc. See CB_starmap02.ani for the proof). As time goes on, and admirals cut their teeth on destroyer tactics, they start using them more and more, finding them much more effective (whether true or not) than their carrier group counterparts.
It is in this way that the destroyer takes over. It's really no different than what happened in WWII. Before the war, admirals were dedicated to the battleship, but when they were forced to use carriers to fight the war (due to Pearl Harbor), they began finding new, more effective ways to fight a war at sea. Thus the battleship was regulated to shore bombardments and the carrier became the jewel. The destroyer came up the same way.