After the Napoleonic wars, a gap opened between the smallest silver coin and the largest copper coin in many countries. Germany was an exception, as it was busy reforming its many coinages into one national currency. Russia was another exception as it offered small silver as well as large copper at the same time. In other countries, the smallest silver was found too small and the largest copper too heavy. In most cases, the small silver coin got in trouble. Some examples:
In France, the 20 centimes was very small and at long last no longer accepted. In the Netherlands, the silver 5 cent was discontinued due to lacking demand. In Belgium, both the copper 10 and the silver 20 were found inconvenient. In Italy, the weight of the silver 20 centesimi was only 1 gram. In Greece, the 20 lepta was was just as light.
In Britain, the 3 pence was just as impopular. What changed the equation was a wave of revolutions in 1840, 1848 and 1870. By 1875, the once heavy coppers had been cut down to acceptable size bronzes. The small silver had disappeared. Countries started experimenting with other mint metals to fill the gap. Belgium was first, replacing its copper 5 and 10 centimes and its silver 20 centimes with copper-nickel coins. Others followed, though not necessarily so radically. The Dutch made only a copper-nickel 5 cent.
Britain did not follow this pattern. Had it done so, the threepence and maybe the penny would have been replaced by a copper-nickel coin. Interestingly, no copper-nickel pattern 3d is known from this period. There are some copper-nickel penny patterns, but they are the same size as the regular coins. My guess is that they were made to try the metal, not to see if the penny could be replaced by a much smaller coin. I suppose that Britain was much less affected by the revolutions (though it had its share of anarcho-pacifists), so its currency appreciated in terms of the other currencies - in the case of the Dutch gulden from about ƒ10 to about ƒ12. That increased the buying power of the threepence enough to keep it more practical. In addition, political discourse made more and more of "splendid isolation", to the point where anything coming from the Europea mainland was found suspicious, probably including copper-nickel coins.
The end result of the diverging trend was that mainland European coins tended to be in more metals and a smaller band of sizes than British coins. The aberration was rectified for the smaller denominations with decimalization, but the relation between shilling and 5p made it impossible to make the larger denominations smaller until the pre-decimal coins were "forgotten".
I think that today, you would be hard-pressed to come up with a circulating coin that is either exceptionally large or exceptionally small. Round US dollars come to mind, but you find them only in gambling halls. Since brass, aluminium and bimetallic coins were added, outsized and undersized coins are neither needed nor accepted.
Peter