If I'm not mistaken, rifle rounds are more deadly due to their increased velocity and the speed they're fired at. They do more damage to the human body.
1. A victim hit by a rifle shot will have more damage done to his or her body then if the victim were hit by a 'smaller' pistol round. I think we can all agree on that.
Actual "stopping power" relies on so many variables, I'm not so sure it's a safe bet to make the assertion. Higher velocity only means more "damage" if the projectile fired is the same (or greater) mass, which isn't the case with many (particularly muh salt rifle) longarm cartridges. You have to keep in mind the formula of "Mass * Acceleration = Force".
As an example, a powerful 5.56x45mm round may have projectiles of 4.1 grams (or 63 grains) whereas 9x19mm (common handgun cartridge) can have projectiles of up to ~8 grams (~124 grains).
The reasoning behind these differences is quite obvious. Rifle cartridges are designed for accurate fire at distance, and heaver/larger projectiles hamper this. Firearms designed for close-in shooting can afford to focus mostly on raw stopping power.
3. Bigger cartridges, faster rate of fire.
Rate of fire is very similar across the board, since this term is purely describing the time it takes to chamber another round after firing a round. I know what you're getting at though, larger magazines do require reloads less - but that's something else entirely separate from the term "rate of fire".
Edit It should also be noted that "stopping power" has a ton of other factors, too, which make it really hard to determine power of cartridges. For instance, a lot of handgun cartridges are designed specifically for self defense purposes and thus are designed to expand and transfer as much of its energy to the target as possible; by contrast, a lot of 'salt rifle' cartridges are designed from a military perspective which are designed with other principal purposes in mind (like piercing armor).
