It's not easy to give a generalized answer for this, but your question already goes into the right direction. There are not many primary sources that dwell on this, but some things can be gathered from what we have.

Any Roman would expect a proper burial after his death, piety required this - and this was a matter taken very seriously - so he or she wouldn't spent the afterlife in a pitiful state, like the shade that Aeneas meets on his journey into the netherworld, forced to spend his death unable to cross the river Styx because he had been denied proper burial. The roads leading to and from Roman legionary fortresses were lined with hundreds upon hundreds of soldier's tombstones (burial inside camp or the surrounding cities was taboo), showing that the legionaries took burying their dead as serious as the civilians back home, at least in peace-time. For a soldier, the expectation of proper burial if he died on campaign would have made death easier to accept if he could expect that instead of being left to rot out in the open, his body would be properly buried or cremated.

In republican and imperial times, a proper burial meant either inhumation or cremation, inhumation becoming popular during the later imperial times. In theory, these were also the options available on campaign, but complicated by a few factors. The Greek philosopher and military theoretician Onosander wrote in the 1st century BC that a good general should bury his dead to keep up morale^1, while Tacitus criticizes a Roman commander who had failed to bury his own dead after his retreat from the territory of the rebellious Frisians^2. So in practice this might have often been less common than desired, as is illustrated by the most famous example of the burial of Roman war dead, which occured almost six years after the soldiers had died. Germanicus was leading his army through Germany when he came close to the site of the Varian disaster, recognizing this he was, according to Tacitus, overcome with "a passionate desire to pay the last tribute to the fallen and their leader, while the whole army present with him were stirred to pity at thought of their kindred, of their friends"^3. Germanicus had the remaining bones buried in mass graves and a funeral mound erected. Generally, Roman soldiers could expect to be buried, on the battlefield or in close proximity, but military necessities, especially following a defeat, meant that this could not be expected to be observed in each case.

We know little of the actual practice of battlefield burial, but this topic comes up in literary sources from time to time. For cremation or burial, they first had to be collected in the same place, as Livius describes after the battle of Numistro against the Carthaginians, where the Romans "burned their own who had been collected into one place"^4, something that is repeated later during the campaign after another battle^5. Pliny remarks that cremation became the preferred method of burial, after it became known that the corpses of those who had died in foreign lands were being dug up again (probably to be plundered).^6 But if the Roman army was known for one thing, it was pragmatism and adaptability, so if the situation made cremation impossible, for various reasons, inhumation was still better than no burial at all, and if the Roman army was known for a second thing, it was digging, so digging a big trench and simply throwing everybody inside wouldn't have been to difficult.

In fact, Lucius Antonius (the unlucky brother of unlucky Mark Anthony) decided to bury his dead during the bellum Perusinum, so that his enemies wouldn't see the funeral pyres and realize his dire situation; and Frontin relates the story of a Roman commander in Hispania who buried his dead overnight instead of cremating them, so that the enemy thought that the Romans had lost none or very little dead when they came on the battlefield the next day finding more of their own dead than Roman ones, and thus thought they had in fact lost the battle^7. Turner^8 also remarks that cremation is both time-consuming as well as something that requires a large amount of fuel (the human body doesn't burn easily) if one truly wants to burn the body (as required for a proper burial by cremation) and not just be left with a smoldering, blackened corpse. The building of appropriate pyres would have required large amounts of wood, something which wasn't available everywhere, as well as a lot of time, a luxury one didn't often have while out on campaign. Commanders (even those of the enemy), tribunes or especially honoured soldiers might get a separate burial and even some kind of monument, but for the masses that was out of the question.

So mass burial, either in a mass grave or on a big pyre, after the dead had been identified and collected - and this must have been no easy task, with often hundreds or thousands of bodies in various stages of decompostion, rigor mortis or bodily integrity! - was the common way of burial while out on campaign, but sometimes even that much wasn't possible. As for ceremony, as important this was to Roman burial custom, especially for the aristocratic families in Rome itself, with great ceremonial processions (pompa funebris), we have hardly any evidence for ceremonies surrounding the burial of the war dead. Valerie Hope concludes that burial was "probably rapid and unceremonious"^9, and for reasons of practicality that probably was the case in most campaigns. A counter-example would be Trajan's Dacian campaign in the year 101, where, after a battle with severe losses, the emperor ordered the erection of an altar to the war dead near Sarmizegetusa and the performance of annual funerary rites for them, but this was as remarkable as it was rare. If you weren't a famous general or aristocrat (like Drusus), you could expect no special treatment. During a military campaign, the focus was on more important things.

This meant that a lot of soldiers lay buried in some foreign land. But for their immediate families as well as their comrades (which is functionally probably close to the same), this was a very inaccessible place for commemoration. People need a place to mourn, even if it is just an empty grave. Consequently, cenotaphs are something that isn't uncommon among Roman funerary monuments. The most famous is probably this one from the legionary camp at Xanten, erected by his comrade (frater, brother) for the centurion Marcus Caelius of the 18th Legion, who died in the battle of the Teutoburg forest ([ce]cidit bello Variano). The monument contains the sad remark that it is allowed to bury his bones in this plot (ossa inferre licebit), should they be found again in the future. Several other tombstones found near camps also mention that someone has been lost while out on campaign, using the phrase bello X desideratus, lost/gone missing during such and such war. This memorial was erected for Aurelius Victor, soldier of the 2nd Italian legion, who was lost during the war against the Goths, 30 years old, by Aurelia Lupula for her dearest husband. So burial in a far-off country didn't mean that funerary rites or the erection of a funerary monument couldn't be performed closer to home.

Different burial traditions are not something I know about, and I'd be surprised if the sources mention something like that, but what we often see ist that different units develop different styles in their tombstones, since they were often done by the same workshop for a specific unit, so for example the auxiliary cavalry units favoured large stelae featuring a warrior on a horse riding down a defeated enemy, contemporary legionary stelae also from Mainz, show little extravagance. Other legions and units have other preferences, and there is lots of change in styles of representation, both over time and over space.

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1. Onasander 36, 1-2: "The general should think about the burial of the dead [...] both a holy act of reverence toward the dead and also a necessary example for the living. For if the dead are not buried, each soldier believes that no care will be taken of his own body".

2. Tac. Ann. 4,73.

3. Tac. Ann. 1,61.

4. Liv. 27,2, 9.

5. Liv. 27,42, 8.

6. Plin. n.h. 7,187.

7. Frontin strat. 2,10, 1.

8. Turner 2010, 56 ff.

9. Hope 2003, 87.

Main sources used:

• V. Hope, Remembering Rome: memory, funerary monuments and the Roman soldier, in H. Williams (ed.) Archaeologies of Remembrance. Death and Memory in Past Societies. (New York 2003) 113-140.

• B.D. Turner, Military Defeats, Casualties of War and the Success of Rome (Diss. Chapel Hill 2010).