Benefits to asymmetry?

This might not be what you had in mind but I think think breaking from x-y symmetry (i.e. knife or dish shape instead of cone / cylinder) would result in ships that would resist kinetics much better both by being harder to hit and having better deflection / area of impact.

edit: Another idea would be to have a ship with a long boom and a counter mass allowing the actual ship to be able to be constantly in a wide arc roll about the center of mass between the ship and the counter mass. Hitting either the ship or the counter mass probably would be quite difficult due to the rotation.

You'll want some sort of symetry in your ship, or engine setup will be a nightmare. Also (as allready mentioned) woe to yow if one of your engines loses thrust.

I still advocate for broadside designs in certain circumstances. A laserstar laid out broadside-fashion with a strong resistojet on the end can allow for 'ok' performance, but maneuvering is tricky.

Of course. But the AI isn't that great with lateral dodging, and it can be a hassle naming individual translation engines for port, starboard, dorsal, and ventral and then lining up the thrust vector so the ship doesn't spin.

It would be nice if we could control engine burns like we can payload-firing cannon in the tactical screen.

I used to agree but now am not 100% sure about this.  If the pattern of misses/error is symmetrical with respect to x/y, but non-uniform (hit probably is highest at intended target and drops off as you go out), then I think there's actually benefit to spreading out vulnerable components so that near-misses at laser #1 are unlikely to hit laser #7 and vice-versa.  Lasers would actually be less vulnerable broadside (obviously, if you had a bunch of laser drones you'ld want them spread out, not tightly clustered).

OTOH broadside is *much* more exposed to damage to fuel tanks, crew, etc.  I believe carriers definitely want to be nose-forward-lateral-dodging if feasible.  I *think* lasers want to be broadside if low-powered-long-range sniping of lasers is the worry, and if you're worried about heavy weapons hitting your lasership it's probably in deep trouble anyway.

I still build my spacecraft in this fashion, even though I do not seem to be in the majority in doing so. Building asymmetrically allows you to have your radiators completely covered. Putting radiators edge-on to the enemy is nice, but they are still exposed and precise weapons or lucky shots would be able to take them out.

Admittedly, I've fantasized about a knife-shaped spacecraft with steeply sloped armor that broadsides enemies with kinetics and possibly has lasers for backup. All of the radiators would be on the reversed side of the spacecraft. It would have trade offs with the traditional cylindrical CDE designs (poor mass ratio) but would probably have its own benefits (small cross section, sloped armor.)

I have also considered what benefit saucer-shaped craft might have.

Asymmetry has another benefit if you're keen on using aerobraking (and let's face it, unless you're a giga-laser dreadnaught with overpowered MPD thrusters you probably NEED to use aerobraking). That advantage is, of course, the opportunity to produce lift- far more than what's achievable with any symmetrical design.