in the late 2nd century the Bosporan Kingdom, A Greek client state of Rome, launched a military campaign against Scythian tribes to the north of them. would the soldiers who carried out this campaign have been using Roman amour, weapons & tactics, or ancient Greek amour, weapons & tactics?

Since this is very far from my usual area of expertise, I can only provide a partial answer; hopefully someone with more knowledge about the Bosporan kingdom will be able to supplement it.

The Bosporan Kingdom was always a hybrid, influenced both by the ancient Greek cities of the Black Sea coast and the tribes of the interior steppes. Its military seems to have been correspondingly heterogeneous.

First, the infantry. Tacitus, describing a war of the mid-first century CE, mentions a force of Bosporan troops "armed on our [Roman] model" (Ann. 12.16). More directly relevant to this question is an inscription honoring a general for his services in Sauromates' Scythian War, which mentions both a Thracian cohort (apparently a detachment of Roman auxiliaries) and a unit of "hoplites." A few decades later, another general was honored for his leadership of a Thracian cohort and unit of hoplites. If the Thracians really were auxiliaries from Thrace (a long-disputed point), we can of course conclude their equipment and tactics followed Roman conventions. It is harder to know what exactly is meant by "hoplite" in this context. Presumably, most of these men were equipped more or less like the infantryman shown on this tombstone - distantly related to Hellenistic models, but nothing resembling the classical Greek hoplite.

The cavalry, recruited largely from the surrounding tribes, were led by local aristocrats. Dio Chrysostom (writing at the end of the first century CE) describes an analogue of one of these men in his half-barbarized costume:

"Suspended from his girdle he had a great cavalry saber, and he was wearing trousers and all the rest of the Scythian costume, and from his shoulders there hung a small black cape of thin material, as is usual with the people of Borysthenes." (Or. 36.7)

Quite a few of the cavalrymen were probably Sarmatians - the same people Marcus Aurelius would fight in the later stages of the Marcomannic Wars, and who were recruited as Roman auxiliaries. Heavy cavalry on their model, of course, would become increasingly important in the Roman army from the second century onward.

So as a short, and provisional, answer to your question: the armies of the Bosporan kingdom looked much more Roman than (classical) Greek - but it probably isn't especially useful to compare them to either, since they evolved in a very different environment and in response to very different enemies.