The Roman army apparently consisted of more cohesive units with better system of command and control. Antiochus' army had a good core, the phalanx, and some of his cavalry was of very good quality. But his army was much more disparate in its origins and like an Achaemenid Persian army, must have been very interesting to communicate and coordinate units from many different lands and tongues.
Although the Cataphracts had an initially devastating effect on the Romans, the latter eventually deployed its reserve cavalry en masse to rout the spent Cataphract assault. This action rendered the Seleucid Phalanx vulnerable on its flank and the final routing of Antiochus.
The Romans exhibited excellent use of combined arms and good improvised tactical deployments in the right place at the right time. It seems that a good proportion of Antiochus' army didn't get into combat (at least not until they routed) and their superior elephants (Asiatic vs. the Roman's African) were a non-factor except at the end where they stampeded (due to Roman missile fire--peltests, archers,etc.), inflicting much disorder among the Seleucid formations.
So what could Antiochus have done differently? He had chosen the battleground, apparently carefully. But his deployment of his mixed army was questionable --the Elephants spread between Phalanx formations, the use of the chariots to initiate the first assault, among his miscalculations. I have doubts that Antiochus turning into the Roman flank instead of attacking the camp would have in-and-of-itself been decisive. The Roman formations and reserves may have proven too flexible for that. I will say that we have few surviving "primary" sources for the battle. The accounts by Livy and Appian seem to account for what we know and both write of it many years after the event.
Although both sides were initially reluctant to go to war, once Antiochus' vanguard was defeated at Thermopylae and the Roman's had crossed the Hellespont, it was the Seleucids who tried to negotiate and the Romans demanding that Antiochus surrender most of Asia Minor---tantamount to ensuring that some final battle was inevitable.
If Antiochus has won, essentially what Slydessertfox concludes, although I think it would be a temporary state of affairs. The Romans, were after all, historically, very sore losers...
