It really would be pointless, and mechanically complex, to have two part rounds for rapid fire machine cannons, with larger guns gaining no real benefit from it either. It's slower to unload, which is an important consideration when swapping different rounds on the fly, as ships clearly do, slower to reload, and has more moving parts that can fail, whereas a simple one part round need only be loaded and fired, or extracted as one object. I would imagine that artillery weapons use fully assembled, cased ammunition for this simple reason. At this caliber, the difference between cased and caseless is something of a moot point. Either way, the shell will be, very, very heavy. Most 120mm rounds weigh approximately 55 pounds today, case, propellant and projectile.
As for cased vs. caseless... Comparatively, in a vacuum, neither would perform much differently in most regards, with one exception, to be noted later. As a baseline comparison, modern artillery and naval guns use semi-combustible cased munitions, with the largest common gun system being 5 inch (127mm), and generally considered to be an automatic weapon in it's own right, firing around 16 to 20 rounds per minute. There's your basic Minmatar gun, right there, albeit in dinosaur form. As for 'small' versus 'large' tank guns... They've gotten progressively larger, not smaller, over the years, from the 75mm to 88mm guns of WWII, to today's 120mm, 125mm and the 140mm concepts that may be in testing. None of the modern guns use two part rounds, and large scale artillery in modern armies use cased, single element rounds as well.
Previous posts regarding large naval guns are entirely correct. Nothing to add there, and large guns are unheard of on modern warships. That's a missile game.
Morphic metals to adjust caliber? Inflatable rounds? The ubiquitous 'nanites' to assemble rounds at obscene rates to feed a fully automatic cannon at hundreds of rounds per minute?... We've already got a solution for the 'problem' these overcomplicated solutions would resolve. Common calibers. Multiple types, same caliber. It's MUCH more sensible to just assume that your quartermaster knows, when you buy rounds for your 1400mm cannons, you will need 1400mm rounds, and he makes the distinction. It's a game simplification that really doesn't need to be over-thought.
As for caseless weapons, there have been a few made, including the H&K G-11, a few small caliber hunting weapons that are little more than novelties, and at least one 20mm rotary cannon that was a test case. There were no significant savings in weight, or vast increases in most areas of performance. The most notable, the G-11, used caseless rounds for one reason; to fire a burst fast enough that the recoil wasn't felt by the shooter until AFTER the rounds had left the barrel. A cased weapon could not achieve the same 2000 rpm burst rate with a smooth action, so H&K went with a caseless 4.7mm round. Effectively, it chambered and fired all three rounds nearly simultaneously when firing three round bursts (sounding like one exceptionally loud shot, at such a high cyclic rate), but performed as a conventional assault rifle in fully automatic fire, at approximately 600 rpm, with similar handing characteristics. Taking this into account, there is a possibility that autocannons are caseless, firing an entire burst at a high cyclic rate using short, caseless rounds to facilitate the chambering and firing of multiple rounds in fewer motions by the guns mechanism. Heat is less of an issue, since a ship will have various means to expel and sink it, reducing the possibility of cookoff, which was one of the key issues of the G-11. However, it is equally likely that autocannons simply use conventional rounds via standard feed mechanisms. I could see a large caliber machine cannon working using the same mechanism as the Aden 30mm cannon, a rotating breech not unlike a revolver to cycle the rounds into the chamber, then tossing the expended case out the side of the weapon in one smooth motion, while simultaneously cycling more up from the feed to be fired. Simple system, happens to work beautifully.
Now, that said, there IS a case to be made for binary propellant systems. By keeping stores of violently incompatible chemical propellant aboard, you'd be able to just load a warhead, then spray the propellant in right behind it. And boom, presto, a caseless, one piece projectile. And no, I haven't missed the 'violently incompatible' part, but it's no more dangerous than packing your hull full of high explosive, armor defeating rounds. If anything gets into the magazine, you're done anyways.
In the final analasys, the question is one of necessity over... I'd almost say style, but we'll go with 'advancement'. Cased munitions are easier to produce and store, less tempramental, and can be loaded and fired efficiently enough using well understood means. Caseless rounds may gain an edge in rapid burst firing, but they're nothing special (despite what sci-fi would have you believe) in all other regards. Considering the Matari 'if it works, it's good' design paradigm, I'd have to call 'conventional' on this one.
Hybrids... That's like comparing a walnut and a duck. They're COMPLETELY different technology. Hybrids are railgun/coilgun systems that use self contained projectiles, no propellant, and a LOT of electricity to launch it.