Is It Always Three Ways?
There are, when you come right down to it, three ways to provide counsel for indigent defendants. The most comprehensive is the Public Defender. Think of this as a sort of parallel to the prosecuting attorney. In an ideal situation the offices will be of similar size (although prosecutors offices tend to be a bit larger because they have additional responsibilities a PD office doesn't) with similar pay. (Note - I said an ideal situation.) A PD office is usually considered a department of the supervising governmental unit and works under a budget from that entity, just like the prosecutors office or the fire department. Sometimes there is a semi-independent board or authority that is charged with supervising the PD office. It may be a State or a local agency, depending on where your are.
A somewhat similar operation is the contract defender organization. This is where a law firm or, more likely, an ad hoc collection of attorneys enter into a contract with the governmental funding unit to provide counsel for indigent defendants. The contract systems I have looked at all involved a flat fee arrangement based on an annual projection with some provisions for exceptional expenses. There are also provisions for conflict of interest situations (e.g. co-defendants with conflicting defenses should not be represented by the same attorney or organization.) Note: PD offices will have similar arrangements with outside attorneys, often on an hourly rate contract.
Finally, there is the assigned or appointed counsel system where private attorneys are assigned cases (or appointed to represent indigent clients - the usage varies from court to court, even within a state), generally by the local court, and are paid after the case is concluded and they submit a bill. (In a long, complicated case there may be provisions to make partial payment before the case is over) Payment is either based on an hourly rate or a flat fee schedule or a combined system where some events are flat fee and others are hourly rated. For an example of the State regulated fee system for assigned counsel, check out this publication from the Ohio Public Defender. Take a look at page 13, in particular. That is, page number 13 - it's about page 16 the way Acrobat Reader numbers pages. For examples of flat fee systems, take a look at this compilation of appointed counsel fees in Michigan, where apparently the counties set both the compensation for indigent trial defense and the systme used. This report is for 2004. Look particularly at the 3rd Circuit, Wayne, the most populous county, and the 6th Circuit, Oakland (which is the second most populous county according the the Census Bureau), and then the 40th Circuit, Lapeer (which is a rural[?] county of moderate population, again according the the Census Bureau.)
So, what's the best system? Damnifino. Speculation and anecdotes to come.