I have a really hard time deciding which ship I could honestly say is my favourite. The core epoch vessels all have a special place in my heart, really. The Brawler, with its bulky design and heavy (for a frigate) armour is incredible when it comes to scaring off light cruisers from flanking larger ships, considering the bristling amount of firepower it can bring to bear. Armed with a pair of Hypervelocity cannons to offset its gimped speed, it can really do some damage. The two universal hardpoints can let it back up that shield-busting firepower with either harpoons or potentially light assault guns. (But probably harpoons.) The vigilance is a right little monster, if put into the hands of a skilled pilot. The oversized medium energy hardpoint, generally best outfitted with a pulse laser, or a phase beam, is an excellent harassing weapon. Backing that up with a Harpoon MRM pod for those opportune moments throughout the battle, it can easily dish out a hell of a lot for the OP cost.
Can't forget those core epoch fighters, either. Not only are they aesthetically pleasing, but they have an excellent balance between weapons, armour, speed, and manoeuvrability. And a wide array of battlefield roles. The broadswords are excellent line fire support fighters, overloading shields and nixing talon or wasp spam. Gladius fighters can honestly go toe to toe with frigates. The warthogs can turn a close battle with a cruiser on its head with an opportune strafing run on its engines, or sides. And the thunders are nightmarishly good when it comes to fast-capping strategic points, and harassing just about anything that isn't overloaded with PD lasers.
The hammerhead and sunder are some of the most interestingly balanced destroyers I've seen in the game, as well. They both look amazing, and offer up interesting tactical opportunities. Bringing to bear four energy hardpoints, best outfitted with tactical lasers, two missile hardpoints (for harpoons!), and a pair of ballistic mediums, which make for good mauler slots, the hammerhead with its accelerated ammo feeder can just churn out devastating, ranged, and accurate armour piercing power. The sheer rapidity with which it can deal out this HE fire, coupled with those harpoons, makes it a devastating finishing vessel, or unshielded target hunter. Not to mention, it can pull up 360* full shields if necessary. The sunder is the same in that regard, but what really sets it apart is the high energy focus ability, and the trio of energy weapons, two medium, and a large. With an autopulse laser, and magazine extensions, plus a pair of antimatter blasters for close-in assault work, this thing can shred through shields, armour ... Well, pretty much whatever you want it to in record time, and with devastating effect. A couple of harpoons, and a similar trio of vulcan cannons can fend off pretty much any missile or fighter threat.
Then you have the falcon, and the eagle. For cruisers, these things are right monsters. You can tell right off the bat, that the falcon is designed around flanking enemy ships, and peppering it with accurate fire, at a bit of a range. The manoeuvring thrusters assist with this admirably, and the higher mobility and top speed seal the deal. A pair of medium ballistic hardpoints let it project heavy anti-shield fire with a pair of hypervelocity cannons, which, backed up by a pair of phase beams, make for a bristling anti-shield battery. A pair of PD lasers, and a pair of harpoon racks for those opportune moments round out the vessel somewhat, but still reinforce the fact that it's a flanking, anti-shield platform. The falcon, in light contrast, is much more brutish in appearance, and has a steeper weapons profile. This makes it much more effective at charging and laying down fire on vessels indiscriminately, allowing for the better use of a pair of heavy needlers, which will almost instantly cause cruisers to disable their shields, fearing hardflux overload. In turn, allowing the single mauler to get to work. This, backed up by a trio of graviton beams, allows it to outrange most hostile ships, and force them to lower their shields. This allows the pair of ion cannons to get some hits in, wreaking havoc, and letting the more assault-oriented destroyers get to work, and those harpoons get some nice scores on enemy hulls. A single LR PD laser facing fore erases the more threatening torpedoes without much effort, and two regular PD lasers to the rear keep the engines clear of missile threats. Two annihilator rocket pods let the vessel lay down a hair of HE fire along with the mauler's shots.
And hell, that's not even taking into account the Conquest (another beautiful, fast, and ruthless craft).
Personally, I want to see a core epoch medium carrier. Preferably cruiser sized. Two hangar bays. That'd likely be my outright favourite.