Before we start talking about warhammers and maces we should define what we mean. In this answer I will be talking about single-handed, short-hafted weapons with either hammer heads or more symetrical, weighted heads (most often flanged). Most warhammers had wooden hafts, many maces had metal halfts from the 15th century on. In particular, I will be talking about them in the later middle ages and early modern period in Europe - the age of plate armour. It is important to be specific because maces of various types have been used for thousands of years, with stone, cast bronze and forged iron heads. Both of these are primarily cavalry weapons - I have not seen evidence for the use of single-handed warhammers on foot in Western Europe in the middle ages or Early Modern period. Not to say it didn't happen, but it was not the primary use of these weapons. For instance, maces and warhammers are not included in late medieval and early modern fencing manuals, and I have not seen illustrations of them used in combat (you do see illustrations of Eastern Europeans and Ottomans carrying long-hafted maces, but these may have been used in two hands; I have studied these less than Western European weapons). I think a simple thought experiment shows why this is the case - imagine dueling with framing hammers - these are not weapons designed for anything other than simple attacks.

Instead, the illustration that you link from Uccello's Battle of San Romano shows the core use of both of these weapons - their use by mounted, generally armoured soldiers to attack other armoured soldiers. Both maces and warhammers would be hung from the saddle and then used once lances were broken or discarded (swords would also be used as secondary weapons). On horseback, fencing as such isn't as important (not that it is a major factor in an infantry melee, necessarily) and the extra height, supportive saddle and near-standing position of the stirrups gives mounted men at arms a good platform to maximize the power of their swing. I should also mention that wrestling, one of the most effective ways to defeat armoured opponents, isn't possible from horseback, which may have made attacking with brute force using armour-piecing weapons even more important than it was on foot (not that foot soldiers didn't use armour piercing weapons, but their typical secondary weapons were swords, not hammers or maces). Both of these are wapons for attacking men in armour. However, there is an important difference. Maces don't have a point, which means while they can smash armour they're not necessarily as good at piecing it straight through. Warhammers, by contrast, have a sharp point opposite the hammer face, and this is exactly how that Italian man at arms is using his hammer in the Uccelo painting. While I know of no details analysis of the force exerted by maces, experiments conducted against armour as well as simple mechanics demonstrate that the best way to penetrate armour is to concentrate a massive amount of force in a single point. The beak of a warhammer can do this better than any other single-handed weapon. However both weapons can hurt people in armour (albeit with difficulty).

Both of these weapons can be highly decorated, or fairly plain, depending upon the individual piece. The wallace collection in London has both this fairly plain warhammer, and this etched and gilt example example. Both of these could be used in warfare - the etching and gilding of the latter would not make it any less lethal. Maces could also be plain or more decorative. However, unlike warhammers maces were used in a purely ceremonial way from a fairly early period - these 15th century maces of the Holy Roman Emperors Frederick and Maximilian look more like contemorary bishop's croziers or even cathedrals than they look like weapons. They even include game boards in their hollow handles! This ceremonial use continues with the ceremonial maces used by royalty, civic institutions and even colleges.

Based on the above, I don't see evidence for a social division in the use of maces versus warhammers. Both are the weapons of cavalry and so, while they are not necessarily 'noble' weapons (most mounted soldiers in the later middle ages had no title, let alone a peerage), they are the weapons of those soldiers wealthy enough to afford a horse and some armour, or socially connected enough to be given these. As to the costs, I have not seen a comparative cost for a 'plain' mace and a 'plain' warhammer. I suspect that you are right that a wooden-hafted hammer would be less expensive than a contemporary 'gothic' mace, but both weapons had a wide variety of 'trim levels' if I can use a modern term. This illustrates an important point about the social history of weapons - the class associations of a weapon are determined not just by the cost of the weapon itself, but also by the context in which the weapon is used. To use another example lances are the weapons of mounted men at arms, and therefor their use is associated with the military aristocracy (and those in lower social orders with pretensions of -joining- the military aristocracy). Never mind that lances themselves are simple weapons - not cheap, necessarily, but not expensive or complex. But economically their use is bound up with the costs of armour, a horse (multiple horses) and the servants required to assist with these. Socially their use is associated with the warrior aristocracy - hence the high status of fighting with lances, as seen in jousting.

Now, there were two-handed weapons used with hammer heads, and other used with spikes, flanges and other mace-like features. The social context and cost of these weapons varied a great deal. Many hammer-headed polearms were pollaxes of one kind or another - weapons often used by dismounted men at arms in both war and sport/judicial combats on foot. These were correspondingly well made and sometimes quite beautifully decorated. On the other hand we see references to English Archers using 'becs de faucon' at Agincourt, and these may have had hammer-heads (they certainly had beaks, hence the name). Two-handed weapons with mace-like heads are less well made and more associated with common soldiers with less money. Both of these types of weapon have wooden hafts unlike many maces and some warhammers from the later middle ages.