Are the Trojans in the Homeric Epics portrayed to speak Greek differently than the Achaeans?

There’s no dialectal difference, although I wouldn’t expect one from an epic poem: Homer is not Aristophanes. Of course, the Iliad is not a documentary, and while the poem concedes that the Trojans’ allies did not speak Greek, it’s doubtful that the actual Trojans of 1200 BC spoke Greek either.

Trojan language – Wikipedia mentions that Hilary Mackie has observed in her monograph Talking Trojan Speech and Community in the Iliad that the style of the Trojans’ speech in the Iliad is different from the Achaeans’:

in simplest terms, Trojans speak poetically, with the aim of avoiding conflict, whereas Achaeans repeatedly engage in public, ritualized abuse that linguists term (from another source) flyting: “Achaeans are proficient at blame, while Trojans perform praise poetry”

So no “Khello Komrade Priamsky, please to drink kykeon wit me” or “Zis is Troy! Ve do not drag ze korpses behint uns!” But something subtler, yes.