About 15 years ago, I read an article somewhere that there was some sort of Director's Guild of America rule that two individuals could not share name credit for directing a film (ie they could not be credited as "Joel Coen and Ethan Coen"). The Wachowskis got around that rule by having the credit read "The Wachowski Brothers" (same with the Hughes brothers).
For whatever reason, the Coen brothers did not want to use the "brother" credit and so agreed to give Joel the Director credit and Ethan the Producer credit. It may also be that since they predated the Wachowskis and the Hughes that they did not challenge the DGA rule in that fashion. I suspect the Wachowskis and Hughes challenged the DGA rule and were allowed to use the "brother" credit as a compromise. The b68Coens probably just continued to use their old practice for credits until the rules changed and two individuals could be credited.

As for their respective credits though, they used to have an agreement that Joel gets the director's credit and Ethan gets the producers, even though in reality they both directed and produced together (there was some kind of problem with double credits, the precise nature of which I can't recall at the moment). As a matter of fact, until now I hadn't even noticed they've been both getting the director's credit starting with The Ladykillers. Wonder how that could happen.
"facts are stupid things" Ronald Reagan

Damn it, took the wrong Coen. My mistake.

What are you talking about? Joel has the director's credit for every one of their movies.
"facts are stupid things" Ronald Reagan