Cruisers are the bulked up heavy-hull ships of STO. Think "Tank" Escorts, being lightweight, fast and able to load dual- and heavy Dual-cannons, mean that they are your DPS ships. Think "Mage" or in the case of the escort-carrier "Hunter". Lastly, Science ships are the healers and support craft. Think "Priest". Doesnt mean that they can't crank out good kill numbers, but it isn't their main role.
Having said all of that, I use my escorts in a fencing style of play. constantly moving, constantly hitting. This enables me to keep from getting hit as much by aoe attks, but also gives me ways to exploit my attacks, while keeping outside the range of most attacks. This is key in fleet battles, however when flying in solo fights, your strategy should be kill them as fast as possible. Most escort ships cannot hold out in a long, drawn-out slugfest.
Scarabpoet pretty much hit the nail on the head with this one. Only thing I'd add is that while in a cruiser you'd normally fight broadside, facing your flank to the enemy to hit with both sets of beams, escorts are more efficient head on (this is why escort pilots often put turrets in the rear).
A lot of escort pilots also stick close to their target (inside 5km), but be careful with that. If you're too close, the exploding enemy will blow you up too, especially if your shields are already down.