If USdollar is currency, it must be both. For the record, there is nothing like a pure currency. USD is definitelly getting less and less currency. Bitcoin is getting more and more currency.

But honestly there is nothing to debate over. Definition of money is:
#1 a medium of exchange
#2 a unit of account
#3 a store of value
#4 standard of deferred payment.
(money is all 4 points at once)

So the logical implication is that if bitcoin (or anything else) has to be a currency, it must be a storage of value and payment system=medium of exchange. Another logical implication is that if you believe that USD does not fulfill all 4 points above, then you do not believe it is a currency. (Maybe you have your own definition what currency is, but then we really have a problem.)

Last remark: far the biggest problem for bitcoin will be #2; everyone thinks in USD or fiat even when using bitcoin. I pay people in btc always based on exchange rate. Their salary is 4K USD, not 10 BTC.