Note: this answer focuses on Northwest Europe, particularly England and France. I use English terms.
The answer is to your question depends upon what you mean by 'common' soldiers and what you mean by the 'rich and noble.' The shortest answer is that full plate armour was, by around 1400, the equipment of men at arms, those soldiers that could fight like 'knightly' heavy cavalry, whether or not they had noble or knightly titles.
To explain more fully, the 14th and early 15th century are the period when full plate armour was developed. While there were some plate defenses that were used in 1300 (coats of plates for the body, couters on the knee, poleyns on the elbow, greaves on the shin), these were a supplement to mail armour, which was the primary defense of the 13th century knight. By 1400, the situation is reversed, and plate armor protects most parts of the body. Mail armour is now used as a supplement for plate as part of the full 'harness' of armour - something to close the gaps the backs of knees and elbows, the neck, the lower hip/upper thigh and (if the cuirass has no backplate) the back. Plate is the primary defense, however. To conclude, in 1300 no one was wearing 'full' plate armour. By 1400 it was the standard equipment of those soldiers who fought in full armour.
Returning to your question, who would wear full armor, whatever that was at the time? All knights and 'men at arms' would own full armour. A man at arms is a man who can fight as a knight, in full armour, on horseback. Sometimes men at arms fought on foot, particularly the English but also the French. The term 'Men at Arms' includes knights and untitled men at arms, many of whom would still be landowners (or the sons of landowners) and many of these would style themselves 'gentlemen.' These people would be 'rich' in terms of being significantly better off than your average farmer, however they weren't necessarily from the truly elite ruling class of titled noblemen - in fact most of them weren't.
During the 'transitional' period of the 14th century, the question of what 'full' armour for a man at arms is somewhat trickier. Some men at arms would have more 'up to date' equipment that included more and better plate armour. For instance, in the third quarter of the 14th century a well equipped man at arms might have a breastplate made of one or two pieces, while a man at arms with older equipment might still use the multi-part coat of plates. Certainly the wealth of the man at arms could play a role in this - noblemen and other wealthy men could afford to buy new armour to keep up with the latest trends, but personal taste also played a role - Tobias Capwell has found that some funerary effigies of very wealthy English knights still show very 'old fashioned' armour.
Different pieces of plate armour were adapted in different orders in different countries - the English were early adopters of fully enclosed arm and leg armour, for instance. So men at arms from different countries in say, 1360, might have different amounts of plate armour as part of their harness. But in general, to be a man at arms was to own a full suit of armour, whatever that meant at the time.
Other medieval soldiers, by contrast, did not generally wear full plate armour. It is much harder to determine exactly how widely used armour was among common infantrymen like English archers and Swiss pikemen, however the general trend is that common soldiers became better armoured as time went on and plate armour became more affordable. Generally, this didn't include full armour for the entire body, but would consist of armour for the arms, torso, and sometimes the upper legs.
Sources: Claude Blair, European Armour 1066-1700
Tobias Capwell, Armour of the English Knight 1400-1450
Alan Williams, The Knight and the Blast Furnace