357 Magnum is significantly faster out of a 2 inch barrel than any 38 Special +P out of a 2 inch barrel when comparing similar bullet weights assuming both cartridge are loaded close to SAAMI MAP. Those ballistics are easy to measure.
http://www.ballisticsbytheinch.com/ will show this fairly well. 35,000 psi of 357 Magnum makes is significantly more potential than only 20,000 psi of 38 Special +P
That said there is a lot of arguments on whether the increase velocity of 357 Magnum make it more effective in a self defense situation especially in the case of snub nose revolvers where both cartridges give up a lot of their potential. The shoot-ability of the snub nose likely plays a significant role in there ability to be employed effectively also beyond simple balistics.
Before I bought my S&W 442 I borrowed a friend's 340PD and after shooting a few 357 Magnums loads through that I quickly realized that an air-weight 357 Magnum was not worth a damn to me. The muzzle blast and painful recoil made it pointless compared to how much better and faster I could shoot a similar weight 38 Special. The extra cost of the gun compared to the S&W 442 I ended up with made the decision easy. Not to mention 38 Special +P performs better in a 38 Special chamber than a 357 Magnum chamber and you need all the help you can get in the short guns.
I always suggest that anyone thinking about buying a 357 Magnum snub nose, especially the air-weight models to go borrow/rent one before you lay down the significant money. Then race to six rounds. Shoot five 38 Special +P as fast as you can and do a reload fire a sixth round. Compare that time to doing the same thing with 357 Magnum. See if you fingers will even let you get the cylinder open to do the reload. Not many shooters can shoot a 357 Magnum snub nose revolvers well enough to justify carrying them.