I for one only marginally believe the science behind barrel porting. Well, it's not that I don't believe it as much as it's been over hyped.
I've written about this extensively over the years so I won't go into a lot of detail but the design of the gun itself will mitigate or increase muzzle rise. The relationship of the thrust line of the barrels to the center of the recoil pad basically dictates how much muzzle rise you will get.
A browning Citori with it's under lug action increases the depth of the receiver and in doing so increases the height of the thrust line in relation to the shoulder. A Beretta with it's side lock up has a more shallow receiver and gets the thrust line closer to the shoulder and in doing so mitigates barrel rise. Barrel porting might help the Browning a bit here and that might be why Browning still offers it on target guns.
Years ago, my friend and I had identical Beretta 686 sporting guns and I decided to port mine as it was all the rage at the time. We shot those guns side by side and could observe absolutely no difference in muzzle rise, mostly because there was little to start with on the bottom barrel, if you shoot this barrel first then muzzle rise on the top barrel matters little anyway.
If you've ever watched someone shooting an old humpback Browning and look closely you will see a lot of muzzle rise. This is because the barrel is so high above the thrust line. More modern semi auto manufacturers made efforts to lower the barrel in the receiver to mitigate muzzle rise and this is apparent on modern semi's with the belly in front of the trigger guard which was necessary to accommodate the magazine. These guns still have some muzzle rise but nothing compared to the old designs. Porting might help muzzle rise somewhat on these guns.
What porting on shotguns does not do is mitigate recoil as some claim. Shotgun barrels are so thin that it's basically impossible to redirect gasses other than 90 degree's from the barrel therefore no recoil reduction occurs as it does on a rifle barrel which is thick enough to direct some thrust back towards the shooter. Heavy recoiling rifles such as the 50 BMG use brakes with gills that provide a lot of surface area to redirect the gasses because just the barrel thickness isn't enough. Also, shotguns run at approximately 11,500 psi compared to rifles which can run as much as 60,000 psi or more, more pressure enables better recoil reduction if you can redirect it.
The weather is too crappy to shoot today and I have to paint a bathroom, I seem to be having trouble getting motivated....