IMO no shotgun in this world is more aesthetically pleasing than a traditional side-by-side with straight stock and splinter foreend. its a proven design with excellent balance that is a joy to hunt with.
We have a winner!
The single shot, however, does have its place in the hunting field. For early season ruffed grouse, the foliage is thick and you will never get a second shot at the bird anyway. A lightweight single shot is a very useful tool under those conditions. Since the shooting is close range a sub gauge gun is advantageous and results in an even lighter, faster gun.
The single shot break action gun, especially with an exposed hammer, is also IMHO the best, safest way to train new hunters. There is never any doubt about whether the gun is loaded or cocked. It promotes good concentration as well - if you have only one shot, you learn to make it count.
While inexpensive and cheaply built single shots dominate the market, there are some better grade guns available. For instance, the Beretta model 412 / 413 folding gun which was made in all gauges.
http://www.berettaweb.com/Beretta_Folding_Shotguns/Beretta_412_series.htm
Just as with a double gun, gun fit is important for a shooter with a single shot. Stock modifications (such as reducing the length of pull for a smaller shooter) are more palletable with an inexpensive single shot than they are with a costlier double. There is little reluctance to "play" with the stock (or the barrel length or choke for that matter) when the very worst that can happen is that you have to go buy another $75 shotgun. When the time comes for a better gun, the shooter will have a much better idea of what stock dimensions will be suitable.
Finally, there are hunters who see the single shot shotgun as the ultimate wingshooting challenge (just like there are riflemen who favour the single shot as the ultimate sporting gun). One shot, one bird, no excuses.
Yes, my first shotgun was a single shot, and yes, my memories of using it in my early years probably affect my opinion somewhat. However, that does not reduce the usefulness of the gun as outlined above.
Sharptail