Do you think the performance in short barrels is advertisment or real based on your experience?
In regards to short barrels ...
Sometimes if not all, the velocity is slower than advertise, and that would hold true to energy as well. Bullet expansion, highly depends on velocity.
Advertisement and personal experience more often than not conflict with each other via random sampling. Based on research and my own findings.
As for advertisement of ammunition I see it as a general idea of what to expect and how it will perform via ballistic gel and nothing more. I don't never take a manufacturer(s) data as full gospel. In other words, I use it as a general guideline and that's about it. Based on what I've seen most of the time... ammunition fails to perform as advertised, but sometimes exceeds the expected results. Knowing this, I look at other aspects for choosing a specific load. ie. ignition reliability, accuracy, casing type (prefer nickel for semi-autos and revolvers), reputation with LE, and so on.
If the performance is real, would that be due to a faster burning powder or how would they achieve that?
I am somewhat familiar with handloading, but I am not a hand loader expert of self defense ammunition and for good reasons not mentioned here. As for the mentioning of a faster burn rate, there is a fair amount of complexity and explanation required. I think that it's a great question you ask, but I think there is a ton of expertise (experienced hand-loaders) on this forum that might have a precise answer to your question.
In the case of self defense ammunition ... it all boils down to firearm reliability, ignition consistency, and shot placement ... regardless of what over-hyped advertisement wants us to believe.
That's all I have, but that is my opinion and two cents worth.