This question is, of course, remarkably late - many moons after Google started supporting the cross-domain canonical link element. But in light of all of the canonical-related questions that have been popping up in this forum, I thought I'd ask. If there are two sites with pages containing the exact same page of content - let's say a news syndication site and the original site containing the article - and both of them have a canonical link pointing to themselves, how does Google determine which one should be indexed/rank first? I've seen a lot of noise re: the Mayday update and this specific issue as well, this seems to be the major SEO issue of 2010.
Here's what should happen, if all systems at Google are firing away properly. The URLs from both domains will be indexed as instructed by the canonical tag on the domain. Then Google's duplicate content filtering will decide which one gets served for any particular query term.
In other words, the canonical link tag is a URL sorter, not a content ownership sorter. If the same company owns both domains, they can use a cross-domain canonical link to instruct Google as to which one is preferred. But when there is separate domain ownership both stating a canonical URL on their domain, it's going to fall into Google's normal duplicate content filtering heuristic.
I think you might be complicating this a bit. Take out the noise -- Mayday, rel canonical -- and you're simply left with two pages with the same content on different domains. As such I'd assume the normal Google algos would apply.
Oops, that's what happens when you go make a pot of coffee in the middle of posting a reply. And tedster says it so much better.