I have some time at the moment and since this topic interests me, I'm going to ramble for awhile about some of the theoretical benefits and disadvantages of the three recoil operated actions. By that, I mean that this shouldn't be considered a thorough or exhaustive analysis of the topic--just my general thoughts on the matter.
A tilting barrel necessitates a larger opening in the front of the slide to accommodate the tilted barrel. The opening in the slide must be slightly oval to allow the barrel to tilt. That is a disadvantage since a tighter opening in the front of the slide provides a theoretical accuracy advantage.
The problem, is that all the rotating barrel actions and locking block actions that I am aware of, require the barrel to be tilted during the normal field-strip disassembly process. So the theoretical advantage is nullified by the practical consideration that some tilt must be accommodated to allow the gun to be field stripped/disassembled.
Most rotating barrel actions require some sort of locking block which adds weight and often results in the barrel being moved higher above the hand contributing to muzzle flip and slower recoil recovery. However, the STI GP6/Grand Power K100 design eliminates this locking block by using a helical cam that bears against a pin. So while the locking block is a disadvantage of most implementations of the rotating barrel actions, it's not an inherent limitation--it can be avoided.
The primary disadvantage of a rotating barrel lockup that I see is that it requires the cartridge/casing to rotate slightly inside the chamber (or rather the chamber has to rotate around the cartridge/casing) during both the feeding and ejection process. The cartridge/casing is held stationary, at least to some extent, by the extractor while the barrel rotates. That means that either the chamber needs to be a little more generous or kept cleaner or there will be more of a tendency to have feeding/extraction issues.
The Walther style swinging locking block actions seem to be a little more fragile than the other two designs which is probably why we never saw an official .357SIG version of the Beretta 96. My hunch is that this is a result of the way that the locking block engages the slide. There are two distinct engagement surfaces/points on either side of the locking block, and if they don't engage precisely the same, one "ear" of the locking block will be stressed more than the other and that can result in early failure.
The locking blocks do take a beating, and even though they are easily replaced, they are expensive enough that it can be a little painful to spring for one. In my opinion people obsess about this more than is warranted, but it is an issue that must be considered.
The other two designs can be set up so that it's easier to get uniform locking engagement so there's less likely to be assymmetrical stresses on the locking surfaces.
The rotating barrel design can be set up to allow the barrel rotation to partially counter the effect of the bullet "torque recoil". The motion of the bullet not only induces linear recoil as a result of the bullet's being propelled forward, it also induces a "twisting" recoil on the barrel (and therefore the gun) as a result of the bullet's being spun by the rifling. The gun twists in the opposite direction of the bullet's rotation. Theoretically, the designer can set things up so that the barrel's rotation during unlocking can counter this at least partially. I don't know how practical this effect is--it may be purely theoretical. I have access to two rotating barrel designs, and one is set up so that the barrel rotates in the same direction as the bullet during unlocking, the other is the opposite.
I suppose it would also be possible for the designer to use the "torque recoil" to help slow unlocking slightly, but again, I don't know if that's really a practical effect. I guess I should run the math to get some insight, but I'm not motivated enough at present to do it.
The tilting barrel lockup does provide a feeding benefit by dipping to make a straighter shot into the chamber from the magazine. That said, examination of the Beretta 92/96 design shows that it's clearly possible to design other styles of lockup to provide a straight shot into the chamber.
What it all comes down to, in my opinion is that the benefits of the rotating barrel and swinging locking block actions aren't really practically significant or are nullified by other design considerations and come with some (perhaps minor) disadvantages.
After mulling it all over, my take is that the tilting barrel design really doesn't have any significant practical disadvantages when one considers real-world implementations of all three designs. Therefore its simplicity and ease of manufacture (especially in its simplest evolutions which eliminate the need for multiple locking surfaces and swinging links) make it the most commonly employed design for recoil-operated locked breech pistols.
