Richard;
Your example would result in a duplicate. In really basic terms, here's what happens:
You have one site with two portal aliases, foo.bar.com and bar.foo.com. They both link to the same index.aspx page. That means the page is accessible at both foo.bar.com/index.aspx and bar.foo.com/index.aspx. Let's say you have 100,000 requests for Widgets each month. 80,000 go to the foo.bar.com/index.aspx page and 20,000 to the bar.foo.index.aspx page. As far as you're concerned, you got 100,000 requests.
As far as a search engine is concerned, you didn't get 100,000 requests. Foo.bar.com got 80,000 and bar.foo.com got 20,000. It seems like a small detail. But if your Widget competitor, giantco.com, has only a single URL that gets 90,000 hits, search engines rank it higher than your site that got 100,000 hits. That's because they see three separate sites, one at 90,000, one at 80,000 and one at 20,000 requests. It gets even more complicated when you have ten competitors who have between 25,000 and 75,000 hits. Then bar.foo.com shows up on the second or third page of a search result, whoich nobody will click on. In effect, 20% of your customers don't count in rating your popularity.
It's not that simple in reality, since a site's relevance to the search is based on a whole lot more than requests, but it is a factor in SEO. The proper solution is redirects, and a 301 will indicate that the redirect is permanent and search engines will then combine the poluarities of each URL for a total popularity. And keep in mind that when everyone talks about SEO, they're really talking about Google ranking, since that's the only metric the general public uncerstands. And there are many ways to affect that ranking beyond 301 redirects.
Jeff