I run 2 DHC + 1 DC (all AP) + 1 Quantum Torp up front
2 Beam arrays (again AP) and a Quantum Torp in back

The beam arrays in the rear do MUCH more dmg than turrets when the enemy isn't in my narrow forward cannon arc. Plus I utilize 2 HYT (usually I and II) so the CD is cut in half (the global cooldown of any HYT is half of the individual ability's).

So I usually alpha strike with my tact captain abilities like Attack Pattern Alpha, my cannon rapid fire III and HYT II.... get really close, then swing around.... punch out a BO I and a HYT I from the rear. Circle back... rinse repeat (if necessary lol). Of course throwing in other random attack patterns are useful too.

Keep in mind DC fire a longer burst which means you have to keep the enemy in your firing arc longer to get the full amount of dmg. DHCs fire short powerful bursts so as long as you can get in range for just 1 sec you'll get off all your shots.

I like the 2 DHC and 1 DC for the power use balance... uses a little less power (higher dps... slightly) yet stick packs that awesome DHC CRF PUNCH!

I run elite STFs with the loadout above with great success

I am also wondering is it better to use dual cannons over heavy cannons in STF Elite's? I see some players able to fire more often but I am not sure if firing more at the Borg is a good thing or a good way to agro them and make them kill me more often since I am the player sitting with 3 dual heavy cannons with a quantum torpedo in the front and two beams in the back with another photon torpedo in the back? I love my DPS and bonus. Like the OP said there is really no real difference in the stats of a dual cannon over a dual heavy cannon what do you all think I should choose?

then why not use all Beams in the rear instead of one and two turrets? I'm probbaly wroing or missing something but wouldn't 3 beam arrays do more damage than 2 tourrets. Or even Two Beams and another Torpedo?

It's b/c you have the option of firing 7 weapons at the same time at one target. 4 fore, 3 aft (turrets). However, they don't do all that much damage as a tradeoff for that 360% firing arc. I just swapped one of my turrets for a Beam Array on the aft so that I can still broadside while circling toward a forward stance to my target.

*Edit
Actually this is getting off-topic, since it's supposed to be all about DC vs DHC.

On-topic: I tried replacing one of my DHCs w/a DC, and it seems that at a closer range, the 3 DHC setup worked better than 1 DC and 2 DHCs. Both were done w/a DBB using Overload and the cannons using Rapidfire. This was PvE, not PvP, mind you.