Wow... OK... lotsa opinions there.
Let's see, where to begin...
aceface, dogfights are for atmospherical combat. If you want realistic space fighter combat, I recommend watching Battlestar Galactica (reboot, not the old one) and Babylon 5. In both series, turning mid-flight to face the opponent chasing you and firing your guns at him, or using directional thrusters to strafe sideways and shoot the crap out of something, are valid and practiced tactics. Sorry to say that, but aeroplane-style dogfights have no real place in a space game with Newtonian physics.
About the weapon vs shield problem: buffing shield capacity could solve some problems. It can be argued that people will just take some shields off and put more guns on, but you seem to forget something. Shield capacitators by themselves, don't cost power, so you can just put on more. The rechargers use power. (one of the reasons behind the system separation) On the opposite side, every single extra weapon block you put on, WILL increase your power consumption as well, so if you want a bigger gun, you gonna need to also add more support, effect, power reactors and power capacitors. Ship size efficiency is already kind of capped with the 1 million e/sec soft cap on power generation. That makes ships power efficient up to about 12K mass. After that, to feed the juice to your systems, you have to place a ton of reactors as well.
Currently, the missiles are the biggest problem as no other weapon is capable of removing millions of shields and core a ship the same time for that block count, and do that from the next sector. I think missile/pulse torpedoes are fairly balanced with their extreme reload time and slow travel speed. Proper point defense can and will prevent them from hitting as well as evasive maneuvers. It's the Missile/beam setups that are problematic as they are extremely hard to shoot down due to their insane travel speed. (almost as fast as cannon projectiles?) There is some balancing at them though as you can't get a lock on jamming ships. But then, the power generation soft cap makes it extremely hard for a big capital ship to run a jammer, maneuver and shoot the same time - they just don't have the generation/block efficiency to do that. If they want to do that, sacrifices must be made in shield capacity, and/or weapon/defense systems, and they still have to manage their power consumption, and watch out for scanner pulses that remove their jammer.
So, if you're afraid of being nuked by a missile, don't go big. Go smart and go smaller, use a ship that can sustain a jammer without sacrificing maneuverability, defensive systems and weaponry. Also, install point defense.
Turret size could be a problem, but in my opinion, the main problem with it is the unified turning speed. Turret turning should be the same as ship turning, based on dimensions and mass. This way the small point defense and anti-fighter turretry can react and track a lot more efficiently, and large turrets would take time to turn onto target and could be evaded with proper maneuvers (and at range, again, jammer. It greatly decreases turret accuracy)
Honestly, I don't see your problems. Build smart. Do your homework. And decide what role you want your ship to take, just like in EVE. If you do that, you'll be fine. Every weapon system in the game has its counters, you only need to find them. They have lock-on sniper missiles and long-range cannons? Use a jammer. They have rapid fire weaponry and swarm missiles? Stay at range and use beam support. They have a lot of turrets? Swarm missile the bastards. But don't whine about how OP weapons are, because your ship isn't prepared for every single possible scenario. Learn to build, learn what to use, how to position, and most importantly, to sometimes disengage and run.