You mean in the sense of a de-facto reserve currency? Well, I expect that, given the dominance of the Iron Bank in Essosi finance, it’s probably the Braavosi currency (which annoyingly we don’t have a name for), at least in the Free Cities. On the other hand, we see golden honors circulating in Volantis, Slaver’s Bay, and Qarth, which suggests competing monetary blocs.
In terms of what the exchange rate is, it’s a bit hard to say. We do know that the golden dragon is much larger than the golden honor or the golden hands that House Gardener minted, due to the consolidation of the entire Westerosi continent and thus the Westerland’s vast gold reserves. On the other hand, Westeros has an undeveloped financial system, so it may be that while dragons are more valuable for their metallic content, Braavosi coins are easier to use in commerce in the east.