Look upon its armament, ye fighter pilots, and despair. The Aeolus is the second most effective cruiser in the game, thanks to its array of flak guns and AAA beams that make attacking it a daunting prospect. The Aeolus will make mincemeat out of an unprepared fighter wing, and going one-on-one with it at short range is a very effective method of commiting suicide. Its anti-capital capability is good for a cruiser with two SGreens; however, it is still incapable of taking on anything larger than itself with any hope of survival. Its anti-capital firepower is theoretically 1/11 that of the Deimos.
It's pretty hard to overestimate the effectiveness of this cruiser... it has, by far, the best anti-fighter capability of any cruiser in the game, and nearly the best of any ship in the game. As far as I'm concerned only the Deimos really outdoes it in that respect. The Aeolus, however, is no super-warship; like all cruisers, it's really ineffective in an anti-capital respect, though superior to most other cruisers. The missions of Freespace 2 are cruel to the Aeolus and do not show its full potential. For example in Clash of the Titans II all of the cruisers were severly damaged, even though at full strength Aeoli can fight off ~ 12 bomber wings and survive. In Their Finest Hour (which also causes many people to doubt the GTVA Colossus) many allied warships failed to have their beams armed, decreasing both their capital-ship weaponry and their anti-fighter defenses.
There is no really no "safe" approach when attacking an Aeolus, so the the only real option is to use slashing attacks: Line up outside its range, charge in at full power, afterburn on the way out and do not turn until at least 1,500m over onto its other side
When an enemy Aeolus arrives in range, there's just one chance to survive: Blow it up, before it blows up you! This thing is horrible for any newcomer in FS and a great threat for anybody else. It has the best anti fighter and bomber capability of all capital ships (I tested this!), so stay away from that ship, if you don't have a friendly capital ship or a volley of Cyclops to deal with it.
While the Aeolus is feared by many as the most powerful anti-fighter cruiser in the game, I must say that it is not. Despite the fact that it has many flak guns (which other Terran cruisers have a complete lack of), the Aeolus has only two anti-fighter beams, while the Leviathan has four. It is not flak that kills people, rather it makes the screen pulse red. This probably gives people the illusion that it is more dangerous than the Leviathan. It does not. Beams are what do the damage; the Leviathan is the triumphant anti-fighter cruiser.
The Aeolus is just about the only FS2 ship that can reliably take down a single fighter. That doesn't sound like much, but one competently-flown bomber can find and exploit a weak spot in almost every other ship. However, despite the Aeolus' fearsome reputation, it can be overwhelmed by a thought-out attack. If you go into FRED and do some testing, you'll notice that it only takes a wing or two of Medusas to kill this 'badass' ship. The exact number depends on the difficulty level, as the bomber's AI is better on higher difficulty.
The Aeolus is a highly effective ship. While the Leviathan does have more beams, beams aren't the whole equation. The Aeolus has virtually a 360 sphere of fire. The Leviathan's anti-fighter weaponry has a far more limited field of fire. Flak is a highly effective weapon. It will eventually bring you down, and is absolutely deadly to larger craft like Ursa which take the full brunt of the impacts.