Battlecruisers trade defensive capabilities for speed. The main thing to remember is that this makes battlecruisers unsuitable for 1v1 against ships of their own size, i.e. battleships. (Although the case of human-piloted battlecruiser vs AI-piloted battleship is somewhat of an exception because human piloting is a significant advantage.)
Battlecruisers fill two roles on the battlefield. The first is punching down, killing cruisers and other ships smaller than themselves through superior firepower. The second is flanking other capitals that are occupied by teammates. In other words, hammer-and-anvil tactics where the battlecruiser is the hammer and the anvil is a proper battleship like Onslaught or Paragon. So it's not like you cannot attack an Onslaught or Paragon with a Conquest, but you need that Onslaught or Paragon to be distracted by one of your teammates first.
The way I fly the Conquest is as a second-line ship behind a battleship, ready to jump in and provide fire support while also preventing cruisers and smaller ships from flanking the battleship. I don't use Escort orders - instead, as a Conquest pilot I'm the escort. And I take to that role loosely, flying around the battlefield supporting whichever of my ships needs support rather than sticking with one ship to protect. If the enemy fleet completely lacks capitals then you don't need to hide behind your own capitals, but can take a more aggressive approach killing ships left and right. A properly outfitted and piloted Conquest has unrivaled damage output and crowd control capabilities.
Compared to the Conquest, the Odyssey has less damage output and weapon range but significantly more speed and a better shield. The Odyssey isn't as good at crowd control, but is better at hit-and-run tactics and can outrun cruiser fleets that are large enough to overwhelm a Conquest. Some say the Odyssey's speed advantage makes it the better playership. I think that's true if you use it to solo things, however in the presence of a supporting fleet the Conquest is at least as good, just in a different way.
As for Conquest loadouts:
You can go with double Gauss Cannons + double Hurricanes (and double Harpoons). This makes for an excellent 2nd-line support ship that can also attempt to kite slow capitals, but has noticeably less DPS than a 900 range weapon loadout, which limits its overall damage output and crowd control ability.
The second option is an asymmetrical DPS-focused build that puts as many big guns as possible on one side of the ship, alongside missiles. This type of loadout is excellent for aggressively flanking capitals and 1v1-ing cruisers. This is the default build strategy for most people.
My favorite loadouts are symmetrical, which is best for crowd control and tactical flexibility, but less good at 1v1. I do find plenty of opportunities to fire both broadsides at once. And I like how when using only one broadside, the flux cost is lower than dissipation which means you can dissipate flux (especially with shields down) and still output damage at the same time. Which is quite useful if you can't risk venting (because venting disables your PD).