The Myth: A smaller caliber bullet can have more stopping power than a bullet twice it's size it the tip of the bullet is rounded instead of pointed.

you cant really measure stoping power but a bullet twice as big will do more dammage if both bullets are at the same speed and all that

ballistics clay

If you stop to think about it, would you rather be struck by two .22 cal bullets or one .44 cal?

This depends a great deal on the construction of the bullet as well as impact velocity. In general I would say the answer is no.

Round nosed FMJ bullets tend to be very stable end penetrate very deep without any yaw or fragmentation.

http://members.aol.com/_ht_a/docgkr/myhomepage/CartDev1860_1940.jpg

Note the wound profile of the 6.5 mm Carcano (same load used to kill JFK). The bullet will tend to penetrate the entire body of an average human in point foreward orientation (unless bone is hit). The result is a wound that is caliber sized.

Pointed bullets have a greater tendency to yaw earlier in the wound path and even without fragmentation will tend to damage more tissue when yawing than the round nose in point foreword orientation.

http://members.aol.com/_ht_a/docgkr/myhomepage/RussianWP.jpg

When a pointed bullet yaws and fragments the wound is substantially larger than either of the above situations. This is the case we see with 5.56 M193, M855, and MK262. Note the large permanent cavity resulting from the combination of fragmentation and temporary cavity.

http://ammo.ar15.com/project/Misc_Images/DocGKR/40052-MilitaryAssaultRifleWPcopy.jpg

As bernie notes, "terminal ballistics" (that is, the study of bullet effect on target) can be rather complicated.
Velocity, mass, construction, and other factors all come into play.
In general, velocity is more important than shape as far as tissue damage goes, but it's also true that most bullets designed for high velocity are pointed as that's a better aerodynamic shape....

But on Weaponology they did ballistics clay tests that proved other wise.

Clay is a poor representation of ballistic performance, regardless of what you saw on Weaponology (I saw the same tests and laughed my butt off). Clay does not have the same texture, composition or elasticity of animal tissue. Ballistic gel is much closer...and even then does not 100% match the real thing. What clay can do is that it gives a spectacular visual result on TV....

If I can add to the excellent post by bernie, bikewer and armynurse . . .

Stopping power is one of those commonly used terms with little real meaning.

Generally speaking what you want is the maximum amount of kinetic energy transfered from the bullet to the target, and transferred in such a manner that it does the most possible tissue damage. Beyond those goals, there are simply way too many variables involved to permit anyone to come up with an objective measure of stopping power. For example, a good sized temporary cavity near a major artery will probably result in a rapidly fatal wound. The same cavity in a muscle mass may have little meaningful effect (as compared to the immediate effects of the permanent cavity). So how do you objectively measure 'stopping power' when bullet placement can make *all* the difference in terminal effects? You can't. That's why things such as the Taylor Knockdown Formula are so silly; good, objective, easily understood, *wrong* data.

The best you can do - as noted so well above - is to use a high velocity bullet that will yaw, fragment to a good degree (the M855 runs about 50% fragmentation) and will not over penetrate (most of the kinetic energy should be tansferred within about 25cm/10 inches to keep it within a torso). As bernie put it so well, in the military world, that pretty much means a pointed round. Couple that *right* round with bullet placement and multiple shots (single, instantaneously incapacitating shots are *not* the norm!), and you achieve that magical thing called stopping power.