There is some convincing evidence to show that the Parthian army of old, such as the royal marshal Surena’s lethal forces at Carrhae, had changed greatly in composition by the time the Antonines came to rule the Empire.

What evidence we have for early Parthian armies heavily stresses their capability as horse-archers, and conversely shows them to perform poorly in close combat. Examples of this include Antiochos III the Great’s successful forcing of the southern Caspian passes when invading Parthia proper; his medium infantry routed the Parthian forces. Equally, they were unable to stand against the Seleucid siege train in the sieges of that particular war.

Antiochos VII Sidetes also prevailed against them in multiple set-piece battles, and though we are unsure of the exact composition of either force in Sidetes’ counterattacks, it is highly likely he fought with a force of heavy infantry and armored lancers. However, when ambushed in the open near Ecbatana by a swift Parthian strike force, Sidetes perished.

At range, though, Parthians were deadly. The horse archer was certainly the key to their success in the field. Carrhae and their skilled harassment of Mark Antony’s invasion of Media display this in full.

As the Parthians settled down, however, they came to resemble the sedentary civilizations they had displaced. This was a common process with steppe conquerors. Their armies became more centered around the armored cataphract lancer — and while this force was certainly formidable, the legions always did better against heavy cavalry than against mobile horse archers. It was a similar story to their success against the Sarmatian lancers and difficulty countering Hunnic forces.

So, in conclusion, their close-contact forces, while still dangerous, represented a familiar and defeatable opponent for Trajan’s imperial legions.

Sources: Peter Green’s incomparable Alexander to Actium (for Seleucid history); Adrian Goldsworthy’s The Complete Roman Army; and How Rome Fell: Death of a Superpower. also by Goldsworthy.

/u/me_gusta_comer is right in describing how we still know very little about Parthia, but there is another element to this that I focused on particularly in my Master’s Thesis. In short, when Parthia controlled the access of luxury trade goods moving between the West (Rome) and the East (China/India), they excelled, besting Rome on the battlefield and expanding their control/imperial holdings. When they lost that iron grip on those luxury goods — whether through an exploitation of the Spice Route (by the Romans and Indians) or Steppe Road (by the nomadic peoples and the Romans) — they faltered, losing battles and imperial holdings to Roman incursions.

Parthia sat upon the main roads for the Silk Road trade between China/India and Rome and was instrumental in its very formation, bringing in massive amounts of wealth to the Parthian Empire at various points in its history. However, there were routes both by Ocean (Silk Route) and by the Steppe (Steppe Road) which provided a path for those same luxury goods and completed excluded Parthia from the exchange. Controlling the flow of trade as a government meant being able to tax those goods and extract wealth from their simple movements, alongside the wealth gained by individuals selling those goods at the expected markup. When Parthia controlled that trade, they essentially got to extract wealth (and other trade goods) from the Romans as the Romans were trying to invade and fight them.

During the early conflicts between Rome and Parthia, the Spice Route trade was essentially dead as Egyptian interest in the trade was long dead and Rome had yet to control Egypt as a province. Similarly, the Steppe Route existed but travelled so few goods that it simply wasn’t worth it in relation to the Silk Road that carried the majority of goods east to west. This gave Parthia a massive advantage in geopolitical relations between the two powers.

With the rise of Augustus, things started to change on both sides of the Parthian Empire. First, east of Parthia the corridor between India and Central Asia, which had historically been ruled by fractious groups became united through the conquests of the new Kushan Empire. Their conquests essentially put them in control of the exit-point from China for all of China’s luxury goods, squarely between Parthia and India (thus controlling the land-based trade of those luxury goods), and in direct control of trade ports on the Indian Ocean where Indian sailors had been mastering the trade winds between India and Arabia. Oh, and based on what we can tell, they didn’t like the Parthian Empire at all.

On the other side, with Egypt under Roman control, Augustus started a massive project to revitalize the Spice Route trade, which very quickly made Alexandria one of the richest cities in the Empire from all the goods flowing through it. The historian Raoul McLaughlin argues that the wealth gained by the Roman Empire from the Spice Route alone allowed them to finance the militaries of the early Roman Imperium and expand their conquests to Briton and Dacia (both provinces that cost more to keep than they made for the empire). I argue that this same wealth, and the declining presence of the Silk Road in Roman discourse indicates that between the Kushans on the east and the Romans on the west, Parthia was being squeezed of the wealth it made from international trade.

The interesting side to all this (or rather one interesting side to all this), is that Rome didn’t stay dominant against Parthia, and they had tremendous problems with the Sassanian Empire (Parthia’s successors) all through that empire’s reign. I argue that in the late 2nd century, during the chaos that the Antonine Plague caused, Rome lost the desire to engage in its maritime Spice Route trade, thus bringing Parthia and the Silk Road to prominence once again. In the Roman-Parthian wars of 216-217, Parthia wins and extracts heavy reparations from the Roman Empire, something that hadn’t happened before. Additionally, with the rise of the Sassanian Empire, the Romans similarly continue to lose territory and influence in the Region as the Sassanian Empire expands theirs. It doesn’t seem like coincidence to me that one of the first acts of the Sassanian Empire was to go east and smash the Kushans, travel west to fight for Armenia (where the Steppe Road wealth flowed through), and eventually in their reign travel to the far end of Arabia to control the trade flowing into the Red Sea.

Now, none of this has anything in particular to say for military tactics, as you ask for in your question. I would argue that in this instance, the difference was not in how the Romans or the Parthians fought, but in how well funded and functional their governments were. McLaughlin argues — and I agree — that the Antonine Plague that killed Roman control of the Spice Route trade was one of the major components in Rome’s eventual decline. Without money to pay troops, pacify subject populaces, and bribe/favor local elites in your favor, it usually matters very little how effective your military tactics are.

If you’re interested in a much more expanded breakdown of this, I can find my thesis somewhere and send it to you. Its a little difficult right now because I’m away from my computer, my books, my actual thesis, etc for the winter break.

Edit: I think it was actually /u/FlavivsAetivs that commented on our lack of knowledge. Oops.

Just to add a more tactical answer:

Later Romans used three tactical adaptations. One was that they were more selective in the site of battle. Carrhae was a massive defeat because Crassus should have never fought there in the first place. Later Roman generals that beat the Parthians forced battle in more hilly terrain that limited or negated the horse archers. The second adaptation is an increase in the number of missile weapons by both legionnaires and auxiliary troops. Legionaries famously carried two pila (javelins) each into battle. Against the Parthians, the Romans brought more pila to throw at the horse archers. They also added auxiliaries who used missile weapons including- and this may sound strange- slingers. Horse archers are VERY vulnerable to missile fire, and this includes rocks. Missiles, not cavalry, are actually the best way to beat horse archers, as horses are big targets and really do not like being shot. These first two adaptations were used to great effect at the Roman victory at the Battle of the Cilician Gates in 39 BC.

The final adaptation is, of course, horse archers of their own, but that really came later. Heavy cavalry don’t do well against horse archers. The horse archers just avoid them, let them get tired, and shoot them until they are dead. The only counters for horse archers are infantry with missile weapons and other horse archers, and it took the Romans a long time to develop horse archers. Learning to shoot a bow is hard, learning to shoot one from a horse is even harder, but they eventually got to where they were a predominantly cavalry army and much of that army was horse archers. The problem was that such an army requiring so much training was hard to replace, and when the Arabs came along and destroyed their army at Yarmouk in 636 AD, the Romans never recovered their military strength. But this adaptation did work out well for the Romans, hundreds of years of success is nothing to sneeze at, and every nation falls eventually.