Hammer, Striker - There are so many solutions -
It Gets No Respect
Tman
May 16, 2013
 
That is what I used to say.  Now, though; it is starting to get somewhat popular. 
I'm speaking of the little .410 shotgun platform and its ammunition.  Oddly enough, the Taurus Judge, a self defense revolver, seemed to have helped bring this new found interest about. 
 
Let me say though: I own an original Judge offering.  It is a fun piece.  Its novelty, the revolver format and short, rifled barrel can also be its drawback when the ballistics are looked at.  When used for up close and personal defense, which is what it is designed for, it looks to be quite effective.  The barrel is short, though, so it is no shotgun and should not be considered as such.  The barrel length combined with the pressure loss due to the typical barrel/cylinder gap associated with some revolvers, prevent traditional shotshells from living up to their rated projectile velocities. Additionally, as you move away beyond a few feet from the muzzle, the barrel rifling tends to splay the shot into an ever widening doughnut pattern.  Such is effective at short range to aid in achieving an actual shot pattern instead of a shot clump but as you move further away it moves radially off target quickly.  So far as any .410 revolver goes, I recommend one stay with its designed use - up close and personal - in this theater it can be very effective. 
 
A lot of Gun Store Cowboys (I dare to say most) will scoff at any actual shotgun smaller than a 12 gauge in the hands of a "Real Man".  I will contend that scatterguns, as a firearm class, should be viewed differently.  I am referring to an actual shotgun; not a handheld revolver.
Modern shotgun size grading should be viewed in a different light than most see it.  The most popular sizes marketed and used in the U.S. these days are labeled as the 12 gauge, 20 gauge and .410 bore varieties.  Incidentally, gauge is an older size reference that gets its definition by comparing how many pure lead spherical balls of the shotgun's bore diameter it would take to equal the mass of one pound.  So, the smaller the gauge number - the larger the associated bore diameter and such the larger the shotgun.  Notice that the .410 is not an actual gauge designation - it bucks the trend and is an actual bore measurement instead.
 
I suggest instead of thinking of these "sizes" as distinctions of power and effectiveness, think of them more as distinctions of firearm weight/bulk and delivered payload capacity.  Examples of the latter can be seen when referring to a manufacturer's shotgun shell chart and making some correlations.  It can be seen that muzzle velocities for similar lead ball shot sizes in the different gauge standard length shells are very similar.  However; the payload (weight or # of pellets) is different. 
 
Stepping back and looking at the big picture, the largest physical size of the selection in this writing is the 12 gauge.  It features a 0.729 inch diameter bore.  The smallest is the .410 which features a 0.410  bore.  For a comparison of similarly described rounds, say a standard length #4 birdshot loading, the 12 gauge shotshell typically carries 1-1/4 ounces of #4 birdshot being pushed to a muzzle velocity of somewhere around 1150 ft/sec.  Likewise, the .410 shotshell carries a payload of 1/2 ounce of #4 birdshot at a similar speed.  The shotshells are loaded with a proportional amount of powder to achieve a powder burn pressure profile that when combined with the different bore diameter's individual face area sizes, a somewhat similar pressure in the 12 gauge pushes more shot weight to the velocity.  But as Newton so wisely stated "for every action there is an equal and opposite reaction" - the 12 gauge launches a larger number of pellets of a given size to a similar velocity but proportionally "kicks" harder in the other direction for its effort.  12 gauge shooters are generally thankful that normally the design of a 12 gauge shotgun uses more material and thus has greater mass which helps dampen this recoil impulse a little bit.  Inertia can sometimes be a good thing.
 
If you can use a smaller payload to get business taken care of, normally you can shoot a smaller amount of the exact same type of payload at a comparable velocity using a 20 gauge or 0.410 bore shotshell in a lighter, more compact weapon than a 12 gauge variety would be.  One can think about it this way: Lets consider two folks shooting skeet. 
Person A is shooting skeet with a 12 gauge shotgun type X using standard length #8 birdshot shells.
Person B is shooting skeet with a .410 bore shotgun type X using standard length #8 birdshot shells.
 
If they break the same number of clays in their match I would have to judge Person B as the better trap shooter.  They were using the same basic setup but Person B used a smaller size gun, launched fewer birdshot pellets and broke just as many clays.  Person B and their weapon were more efficient at getting the job done.
 
Sometimes you need the larger payload and are willing to carry the heavier weapon and bear the brunt of its recoil.  Sometimes you don't and aren't.  It just depends on the task at hand and experience desired.   A shotgun, like any other firearm,  is just a tool for a purpose.  Bigger is not always better but with shotguns it does tend to bark louder, bite harder and break things more effectively.  But this goes both ways...