Plasma carronades are basically the Aurora shotgun. Great for huge damage up close, but drops off really quickly. Basically, the best use I've seen for them is jump-point defence.
IIRC microwaves have a chance to disable electronics, so good for crippling an enemy with less chance of blowing it up.
Particle beams used to be called particle torpedos, and I haven't used them since the first couple of games I played. Mostly all I remember is that you couldn't turret them, but I think they were okay damage, fairly long range; less than lasers, but without the damage fall off. That said, I'm really not certain on that point.
The particle torps (Because beams don't act like that) are basically your long-ranged EW. They get upwards of 1m km range at the high end of their branch of the tech tree, and do pretty decent damage.
Yeah, MW are essentially Electronic Warfare weapons, in that they cripple sensors, fire control, and other things.
One use for carronades I have is to load some onto a light cruiser-ish sized design and give it as good a Vmax as I can, so they can do the interstellar equivalent of running up and bashing people in the face with a sledgehammer. You can also consider using a few high calibre ones as part of the primary armament on beam-heavy cap ships, or as a nasty last ditch surprise on missile ships. I believe that once you hit the end of their tech, the 80cm carronades do something like 168dmg per hit, which is enough to one-shot most smaller ships. A few hits from that sort of firepower would probably plow through even things like hives.
Question: Is it worth loading a ship with a veritable shitton of low-accuracy high firepower 10cm gauss turrets? Because I figure a quad gauss turret with 5sec ROF and 32 shots per volley, even with 17% accuracy, could be mighty lethal. 10 of those turrets (armored) would only require 2,300 tons, and would put out 320 1-dmg shots every five seconds. At 17% accuracy, that is an average of 54.4 hits every five seconds, which equates to 54.4 dmg (on average) per combat turn. If I did my maths right, that would mean 3840 shots and 652.8 dmg per minute, 230,400 shots and 39,168 dmg per hour. Is this actually worthwhile?