I think the only way you'd really be able to measure that is if they were both hooked up to something like a strain gauge so you'd be comparing the two at equal pressure.
Whenever you square the shoulder off and take the taper out of a case it does a good job of hiding pressure and then you add in the fact some brass, like Lapua and a couple others, can take a lot of abuse before it starts loosening primer pockets so these AI'd or "improved" cases get run at, much, higher pressures than their parent case that has more case taper and a shallower shoulder angle so it makes the "improved" versions appear as though they're so much more efficient because they're gaining 3-400fps with only a relatively minimal increase in powder.
I recently built a 222 with a 21.5" barrel. I have only began to work up loads, testing powders, and working with one bullet, a 52 grain flat base in a 1-14 twist Shilen SM barrel.
But I have been around a while and understand the ability of any 222 case to take pressure. Trust me the load manuals are anemic at around 48000 cup as max.
But even in the Superior cases from Lapua, I have ran this little duesh to a little over 3250 fps, and have to ask if you realy think you can get anywhere around 3650 fps improving this case with any length barrel?
In reality I don't think you could get 3400 fps and load the case again, you'd be hard pressed to get a primer to stay in the pocket, let alone seal!
Sorry but 300- 400 fps more over what is capable in the original case is delusional! In all reality I think you'd have trouble getting another 100 fps over what I have gotten with any barrel length, and retain brass for more than couple loadings!
That's just my honest opinion, and from my experience, there are a lot of cartridges that the only benefit improving the case is running it at high pressure without the need to trim as often.
But far to many makes claims that those that have not been there belive! Trust me, I've been there, and increasing the ability of this factory spec case by 100 fps is a stretch, I would be surprised to see 3400 fps with a 52 grain bullet in that same length barrel.