First, I want to mention that to my experience, there can be no easy loading and a powerful shot. That goes for band guns and pneumatics. Its is just something one has to get used to.
Second, loading effort is calculated like so: 20 atm pressure is about 20.6 kilos per square centimeter. Lets say it is your gun pressure. That, multiplied to the area of the piston, results the loading effort.
So, 20,66*0.949=19,6kilos for 11mm barrel and 20,66*1,326=27.39kilos for 13mm barrel.
So the advantage for 13mm is great power at low pressure, and the gun is generaly not strained. So, add a dry barrel to that, and, wow!
I agree with the math, but I tend to disagree with the real world usage - at least for "advanced spearos".
Allow me to explain as I have had this discussion both here and elsewhere but in short, I think most of us - after a while - load our guns at the pressure that we feel we can comfortably load for a long session of spearing. E.g. my 11mm One Air is loaded to about 29bar whereas my 13mm Seac sits about 10 bar lower. Maybe some beginners just leave the gun as it comes from the factory irrespective of barrel size, I don't know. But to me, it doesn't really make sense to compare guns with different piston diameters while keeping the same pressure.
With a bit more experience since I first started this thread and with the help and input of other spearos here, my conclusion is that there is no real world difference between a 13mm and an 11mm gun if they are both dry muzzled and pressurized to the max loading effort the user can handle.
One thing I do know by now, is that spear thickness and length of the gun plays a big role for me in how much I can pressurize a gun and still be able to comfortably load it.
I have seen some builders/tinkerers say that a 12mm piston is "the best", but I have yet to get an answer to why they feel that is. Maybe they reckon it the best compromise between piston weight, o-ring friction and compression ratio but I don't actually know. Again, in the real world, there is probably very little difference between 11-14mm barrel guns if they are all dry muzzled and all pumped up to have equal loading efforts.