I have some problems with the premises of this question, but I’ll try to answer it as best I can. Hopefully I don’t end up answering the question I wish you’d asked, rather than the one you actually asked! I should also say right at the beginning that although I’m good on Roman religion, my knowledge of religion in Ancient Greece is patchy so I’m not going to address that side of the question. In terms of how I’m going to approach this topic it’s actually not a problem – one of the premises of the question that I find problematic is the idea that there were these two separate things called ‘Greek culture’ and ‘Roman culture’ that can be compared and contrasted as neat, bounded entities. It’s probably too much of a tangent for me to address that properly here – perhaps we can go into it later if someone is interested.

OK, so let’s focus on Mars. He seems to have been worshipped at Rome from very early on, although the evidence for archaic Rome is not good. Later Romans would have us believe that the whole edifice of Roman religion was invented by Romulus and Numa, the first two legendary kings of Rome. This includes the worship of Mars – Livy (1.20), Plutarch (Numa 13) and Dionysius of Halicarnassus (2.70) all attribute the foundation of either one or both major priesthoods of Mars (the flamines Martialis and the Salii) to Numa. The major problem here is that all these writers, and indeed all the information we have on archaic Rome, come from much later – no earlier than the 1st century BC. They were not writing what we would call an ‘accurate’ history of the city’s early history but were using these descriptions to define Roman culture for themselves and their contemporaries, and to debate its problems and peculiarities. Again, probably too much of a tangent to go into too much detail here but suffice to say that the literary record on Rome’s early history must be read very, very carefully. Nevertheless, we have no reason to doubt the fact that Mars was worshipped in early republican Rome by dedicated priesthoods, and that this worship was connected to the army.

However, the Roman association of Mars with war was more complicated than just the overseer of battles and armies. He was more closely connected with the purification and protection of the army, and by extension the whole city. The major festivals for Mars were clustered in March (the month named after him), at the beginning of the campaign season, and October at the end. In the March festivals, Mars was asked to protect the soldiers and their equipment in the coming battles, and in October the rituals remove any spiritual pollution picked up over the summer, thereby protecting the army and the city as a whole. It’s important to remember that for the entire republican period there was no professional Roman army – all the soldiers were conscripted citizens who were drafted for particular campaigns and then disbanded once they were no longer needed. Hence the close connection between the army and Rome more generally – the army was the citizenry and vice versa.

This connection with the ordinary citizenry brings us onto Mars’ other main area of influence in Roman religion: agriculture. Cato the Elder, in his handbook on agriculture, makes it very clear that Mars was called upon to protect farmland, and that specific sacrifices were expected before using land for the first time. Again, Mars is being called on as a protector and purifier and is worshipped using the same rituals that were used to purify the army before going into battle. It’s interesting that Cato specifies that the sacrifices be offered to a particular version of Mars – Mars Pater or Father Mars. This is almost certainly a reference to the fact that Mars was supposedly the father of Romulus and Remus (having raped their mother), and therefore symbolically the father of the whole Roman people.

So, we’ve got a relatively clear picture in the republican period of Mars as a protecting and purifying god, connected with the army as a god of war, but also presiding over farmland and the population of Rome in general. I’m not quite sure where you’re getting the idea that Mars represented wars that brought peace – I can’t really think of any specific ancient sources that discuss him like that, although I’d love you to point me in their direction!

I wonder if the question as you’ve asked it is actually more to do with Roman attitudes towards and justifications of their own wars of imperial conquest, rather than being specifically about the god Mars. It is certainly true that from at least the first century BC, the Romans were starting to think about why they go to war and the ways in which they have conquered their empire. In his speech on the Lex Manilia, Cicero gives hints that the idea of so-called ‘defensive imperialism’ is already being bounced around, suggesting that the Romans waged war on their enemies to ensure security, peace and prosperity for themselves and their allies. This idea gets a huge boost under Augustus after 27 BC, once he’s ended the civil wars and installed himself as the first emperor. From then on Rome supposedly entered a new Golden Age of peace – the Pax Augusta – free from strife and bloodshed. The job of the army now was to preserve the peace, even if that often still meant fighting offensive campaigns against the barbarians outside the Roman frontiers. The Roman historian Tacitus criticises the obvious paradox in this image – into the mouth of Calcagus, leader of the Caledonian resistance to the Roman invasion of Scotland, he puts the now-infamous words: “To robbery, slaughter, plunder, they give the lying name of empire; they make a desert and call it peace.”