Gauss Rail Gun: Pretty straight forward. It's a cannon that does damage. The problem is it's a very high antimatter cost and the damage has to go through mitigation shields, meaning the 800 damage level 3 gun really does about 400 damage, maybe 300 if the ship is damaged enough.
Don't leave this on autocast, and don't use this ability too much because it's a waste of antimatter.
It's not a waste of anti matter, but you do have to be careful with it. You can fire it repeatedly if you're using Finest Hour. Other than that, it's good to use as the opening shot against an enemy capital before his mitigation gets run up. All that said, I do tend to favor flak burst over gauss cannon, but I find both useful.
Flak Burst: Again, pretty straight forward. It's a flak burst fired and it does damage to fighters/bombers. It's an area of effect weapon. It's a nice case-specific ability, but I don't use it often. It doesn't kill fighters in one shot, but 3 or 4 shots from this will do it. It's a nice counter to someone who's spamming fighters/bombers.
At level 1 and level 2, it's not too impressive, but at level 3 I find that it's awesome. I gotta disagree about leaving it on autocast; I never, ever do that no matter how many strikecraft my enemy has. The trick to this ability is to wait until a large number of strikecraft are in the AoE before firing it. At level 3, it can insta-gib Advent interceptors and generally do major harm to all others. As an anti-strikecraft ability, I find it to be significantly more effective than Magnetize. Also, since destroying strikecraft gives your caps a miniscule amount of experience, you can actually level low end capital ships pretty quick shooting down strikecraft with this.
Ion Bolt: Another ability with bad payoff for the antimatter you pay to use it, but then again, until you have armistice there's nothing else that you're really going to be using antimatter for on this ship.
I find Ion Bolt to be quite handy. You really can't perma-stun with it, but if you're chasing an enemy cap I'm usually glad to have it. Combine this with Designate Target from your Cielos, and enemy caps are dead meat. It's especially nice to use when he's almost got his phase drive charged up, since it interrupts the jump sequence.
Shield Restore: This ability raises a very large amount of shields, larger than most frigates or curisers offer, so while this ability can be used on smaller ships, it's really designed for other caps. With this ability, your other caps aren't going to die, but t his requires proper monitoring and microing.
Combine this with a Kol that has Finest Hour / Adaptive forcefield and some Cielo command cruisers for Embolden. The Kol simply can't die under those conditions. It can literally absorb the fire of an entire fleet for an extended period of time while it deals back splash damage and gauss cannon shots with all the AM Finest Hour provides.
Destabilizer Charge: I love this ability. It does some damage, sure, but the antimatter removing ability is what sells me. You can remove antimatter from your enemy's cap, so useful in early game.
Area effect anti matter depletion and area effect shield disruption. This ability is under-appreciated and it is awesome to have. It is one of the few viable ways a TEC player can counter Subverters, Overseers, and Guardians. You use EMP charge in the opening phases of the battle to remove enemy support cruisers anti-matter. The shield disruption is icing, but it's nice to have.
Overall, the Dunov is a bit of a soft target as far as caps go, but it's abilities rock. Get two Dunovs to lead your fleet and if the enemy focus fires one of them, it's consort can recharge its shields. Get some Cielos and Hoshikos to up its shields, weapons, and fix the hull and it can have some decent staying power. Nothing like a Kol, obviously, but still pretty darned good.
Radiation Bomb: Not as effective as you'd think it'd be. I've never seen this do too much damage. It's not a bad ability, it just doesn't do much.
Don't turn this on autocast ever. Manually use it in a 1 v 1 ship battle, other than that, never.
Keep in mind that Radiation Bomb is area effect. You certainly shouldn't expect to destroy whole swaths of frigates with this by itself, but the area effect damage it does can 'soften up' a formation of enemy ships. Gotta disagree about autocast. I tend to leave it on and have generated good results. The AI is actually pretty good about firing it into crowds of enemies where it can work the best.
Incendiary shells is nice in conjunction with Radiation Bomb. You can get some serious area effect, DoT damage effects going with those two abilities.
And yes, Raze Planet is ridiculously awesome. Two Marzas with even just level 2 Raze Planet can crush all but the most fortified worlds.
Also, I find that Missile Barrage is quite good if you use it for what it's intended for. In keeping with the theme of area effect attacks, Missile Barrage is good softening up an enemy fleet.