They function similarly, and are sometimes represented as 1d2, but they have the additional aesthetic of currency (whether used as currency or not), which dice don't have.
I've played around with the idea of having dice be a resource in different game prototypes, but I haven't hit on a good implementation yet that makes it appealing to gamers. Lots of people are conditioned by existing game designs to equate "more dice" with "better" in pretty much all cases, even if one were to offer an incentive for trading in dice. Using coins would leverage the inherent "spendiness" of money to maybe overcome that.
