Only thing is that I never really saw the reason behind non-semetrical ships. I mean okay, if the mass was left-right balanced that's one thing, but some don't look that way. (even if they look cool).
Benefits? I could maybe see turning/cornering one way versus another as being faster, but wouldn't the constant need for the pilot to re-orient himself counter that? And what about the enemy... wouldn't they quickly learn to identify such traits and use them to their own advantage?
Remember that one model of "pancake" cat-ship that could only turn left due to a design flaw? If the cat wanted to go right they had to rotate 180 degrees and then go left (it only seemed like a "right" turn to us if we didn't go upside-down as well.
And structurally speaking, if the ship isn't left-right balanced, wouldn't that mean that all stress lines (due to various maneuvers and jumping) would be off-center and at strange angles, and additional reinforcements to keep the ship from breaking in two during certain maneuvers (providing it had a stress build-up)?
To a degree you can deviate from a left-right mass difference by sticking different engines on each side... heavier side getting heavier engines to compensate, so that natural acceleration is straight forward.
Examples: wc3's Paktahn would seem to have this left-right turn rate issue. As would the Strakha. Would seem to explain some of the evasive flight patterns of these ships (game programming aside at least... they did seem to suffer that "tends to turn x-direction" type flaw when I played). Its kind of hard to see pilots being trained to hold the joystick 5 degrees off center in order to fly straight (or have a computer auto-correct such a thing).
... At least wc3's Bloodfang had balanced engines, and its larger wing was compensated by an additional smaller wing on the other side, and so on (such that its natural balance was down the middle).
Oh well... maybe they figured it was just easier. Rather than have pilots have to think which way to evade it was easier to simply drill them to always go one particular direction... or maybe its neurological/psychological... they just tend to go left instead of right, so they figured "what the hell, we're gonna do it anyways, why not build the fighter to take advantage of that natural instinct".