Ease of handling (and effective rate of fire).
You wrote that blanket-statement with little, to no, knowledge of ballistics. Your second item alone invalidates your claim because "stopping power" is a very subjective (basically marketing lingo) statement: a .22 pistol to the head has more stopping power than a .227 to the torso, and your off-the-shelf hunting shotgun has more short-range stopping power (to almost any part of the body) than both of them.
(Read up on Mafia killings; more people were killed by .22 caliber pistols than all other guns, including the infamous Tommy Gun.)
"Stopping Power" should never be used to compare weapons without specifying conditions, and even then breaks down to so many sub-components: ammunition used, velocity, kinetic energy, etc.
An assault rifle firing a full metal jacket round at a torso has a high probability of completely passing through the body. A .357 magnum pistol firing a hollow-point round into the torso is going to mushroom out and expand in the body, increasing the chances of hitting something major.
You can get a handgun that would fire magnum high caliber rounds, but not 20+ at a time, plus only very skilled marksman would be able to shoot such handgun more than one round at a time and maintain any kind of accuracy.
Your statement suggests that only a 'handgun' requires a marksman to maintain any kind of accuracy with sustained firepower; this is completely false.
Have you ever seen the video of an inexperienced insurgent, or gang-banger, shooting an off-the-shelf, cheap, mass-manufactured AK-47 variant? The saying: "couldn't hit the broadside of a barn" wasn't just termed for high-caliber pistols.
If you'd ever attempted to "spray-and-pray" with a cheap mass-manufactured (most commonly found) full-auto assault rifle, you would realize how off your statement is. Your first round could possibly (with luck that any sight adjusting ever happened) be on target, and each successive round would be farther and farther from even being close. Someone taking a second to aim a single pistol round has as much of a chance as the non-experienced, lead-trigger assaulter.
And if you aren't talking about full-auto, then you're "20+ at a time" is way off-base for even the fastest-trigger expert.
There is absolutely no point denying that semi-automatic rifle is by far more deadlier weapon than any comparable handgun.
Semi-automatic rifles are only superior in specific conditions, and even then it depends on the actual weapon, as well as the experience of the person wielding it.
In close range, in a building, etc., the cumbersome non-compact, standard assault rifle can become more of a hindrance than an asset. I would probably take a shotgun, or even a quality handgun over an assault rifle in such an example.