The Austrian Economics Center blog has a post by Finbar Feehan-Fitzgerald on "Hayek versus Friedman: Concurrent Currencies." (The center is located in Vienna, hence it is Austrian by geography as well as by school of thought. I came to the post via a link from Jonathan Finegold's blog, Economic Thought.) As Feehan-Fitzgerald summarizes their disagreement, Hayek thought that the costs of switching currencies were small, hence competing units of account was a realistic possibility. Friedman thought the costs were large, hence a single unit of account should dominate and fend off rivals unless it becomes quite unstable.
Part of the difference between them, I suspect, was what they explicitly or implicitly counted in the costs of switching. A truly level playing field among currencies is rare. The government typically favors its own currency by making all of own domestic payments in that currency and not giving people the choice of payment in another unit; by requiring taxes to be paid in local currency; by requiring in the case of some countries that all private-sector salaries likewise be paid in local currency; and, often, by provisions of the tax code, other laws, exchange controls, and regulations on financial institutions. The result is to create a minimum level of demand for local currency that might not exist in the absence of those laws and regulations. (In fact, I think it would make a good master's thesis to ferret out all of the laws and regulations that tilt the playing field in a particular country and to explain just how they do so.)
Where the playing field is so heavily tilted, a substantial depreciation of the local currency is usually necessary to induce a partial switch to a foreign currency–partial dollarization, so called whether or not the foreign currency is the U.S. dollar. In dollarized countries, local currency continues to circulate and be used as a medium of exchange for small retail payments, but yields to the foreign currency as a store of value and as a unit of account for large payments. Foreign-currency deposits, if legal, are preferred to local-currency deposits as stores of value. House and car prices are typically denominated in foreign currency, even if officially it is illegal.
Once dollarization occurs, it can persist even if the local currency becomes more stable, a phenomenon dubbed hysteresis. Hysteresis seems to support Friedman, but I think it really supports Hayek because under partial dollarization, the playing field almost always remains tilted toward the local currency. It isn't that switching back is hard, it's that distrust of the local currency lingers and people prefer some foreign currency as a hedge despite all the legal advantages to holding domestic currency.
There are plenty of examples of partial, unofficial dollarization. Some occur because of instability in the local currency. Others occur because of trade links: the U.S. dollar is widely accepted in Caribbean countries that have good local currencies because merchants catering to the tourist trade find it advantageous. The latter cases are to me another piece of evidence suggesting that the costs of switching currencies are low in the absence of legal restrictions, but in practice typically high because restrictions are common.
The hypothetical monetary system Hayek envisioned in in Denationalisation of Money has constant, vigorous competition among units of account even within small areas such as a single city. In contrast, I would expect one unit to dominate withing small areas, though perhaps multiple units having large world market shares, providing a possibility of switching if the local unit becomes bad. The computer age opens up new possibilities here that did not exist until recently, though. As we move to all-electronic payments, switching from one unit of account to another becomes as easy as pushing a button, even for retail buyers and investors. It is another case where Hayek looks less like a speculative theorist and more like a visionary as time passes.