The Beretta PX4 Storm and the Grand Power K100/Q100 series have a rotating barrel arrangement as opposed to a more conventional design. The PX4 had some early issues but current production examples seem to be reasonably reliable and accurate.
So do the disadvantages outweigh the advantages in such a design?
It's not that different. In the more common tilt-locking design, the barrel rotates on the pitch axis. In a rotating barrel design, it rotates on the roll axis. They both lock to the slide, they both accelerate while locked to the slide a short distance, they both stop against the frame, and the slide unlocks both by impinging it against a cam surface in the frame.
The rotating barrel, by the way, is also a Browning invention.
The performance will be more a function of the design's other details and the manufacturer's attention than it will be a function of which axis the barrel rotates on.
There are a number of small pros and cons.
A rotating barrel will sit lower in the slide than a tilting barrel. This means that the rotating barrel will have potentially a lower bore axis, but slightly greater sight offset. In any event, most production rotating barrel pistols (PX-4, QSZ-92, Grand Power) are all hammer-fired and not particularly designed for low bore axis, making this potential advantage irrelevant. Colt did have a striker-fired rotating barrel pistol, but it was an enormous pile of shit that never worked. Grand Power does have a striker-fired pistol now, but the frame design is no different than their old hammer-fired design.
A rotating barrel can also sit closer to the feed position of the ammunition when in battery. A tilting barrel's breech end drops down, which wastes a small amount of height, which in turn either drives the bore axis up or drives the entire pistol height higher for a given ammunition capacity.
Rotating barrel pistols usually have the locking elements arranged on the sides of the barrel, and after they rotate they need space inside the slide in order for the slide to reciprocate. This usually makes the slides wider than they would be in tilting barrel pistols, but the difference is slight as most tilting barrel pistols have a significant amount of wasted dead space inside the slide anyway.
In a rotating barrel pistol, the barrel remains parallel to the direction of travel of the slide during extraction and ejection. In tilting barrel pistols the case is being pulled out of the firing chamber slightly off-axis. This problem is worse in compact models, since the height of the locking surfaces is the same but the lever arm is shorter. In practice, this doesn't appear to matter much. Oddly, the Beretta PX-4 subcompact model is a tilting barrel design, and the off-axis extraction should be worst in the subcompact model. So this problem is clearly not a design priority.
There are people who claim that rotating barrel pistols have lower recoil and greater accuracy. These people don't know how physics works and you should ignore them.
The overwhelming majority of new designs have been tilt-lockers, but this has more to do with designers blindly copying the Glock than it has to do with any inherent superiority of that design. I would love to see a rotating barrel pistol design that's as well-made and well-designed as a Glock... but realistically, it would pretty much be just like a Glock, except that the barrel rotates on the roll axis rather than the pitch axis.
First to derail! On a somewhat related note: These firearms are rotary-barrel-delayed. Were there attempts to create firearms actuated by barrel rotation (as the bullet is pushed through the rifling and made to spin, it creates a counter-force that tries to rotate the barrel in opposite direction), where a barrel outfitted with a set of appropriately-designed cams would, by its rotation, accelerate the bolt carrier?
Bolt carrier... in a pistol? Maybe in some obscure, turn of the last century design back before anyone knew what they were doing, but most automatic pistols don't have bolt carriers.
Supposedly the Jordanian JAWS pistol and the Chinese QX-04 both use the old Savage-Searle breech design, but I've never seen either one and Jane's has been wrong before. I'm not sure if that's what you mean; your terminology isn't exactly English idiomatic.