In terms of ballistics, there is a significant difference between the .38 +p and the .357 mag. I shoot all 3 loads out of my revolver and it is almost like shooting a different gun going from even the hotter +P loads to the .357 magnum cartridges.
This info was taken from the Remington website - there are a lot of different sources for this info, but this is a pretty good guideline and really demonstrates the differences on paper.
.38 spl +P 125 grain JHP Muzzle Velocity = 975 fps Muzzle Energy = 264 ft/lbs
.357 mag 125 grain JHP Muzzle Velocity = 1450 fps Muzzle Engergy = 583 ft/lbs
Obviously, there are a lot of other factors that go into caliber choice for a carry weapon such as confidence in the caliber, ability to handle recoil, muzzle blast, noise, etc. that go beyond velocity or energy. Personally, I would not subject my hand to the torture of shooting full house magnum loads out of a 2" snubbie, nor would I feel confident that I could hit anything with it past 5 yds. I shoot a 4" revolver and the recoil is very manageable in that size, but it doesn't make a great carry gun. This may be more info than you wanted. Hopefully it helps out some.