Having duplicate content on different domains is not necessarily a problem that leads to inferior rankings. Depending on the context, Google choses which domain to show in the search results.
Copied content in the web is annoying but usual. A great deal of those cases where content is scraped from other sites relates to product descriptions that can be found in online shops. As a result, duplicate content is generated, meaning that Google or other search engines have more than one version of an identical text in their index. As a basic rule for SEO, duplicate content should be avoided - this is true on a specific website as well as on different domains.
When analyzing duplicate content, the context and circumstances have to be taken into account. John Mueller from Google explained that in last week's English Webmaster Hangout. A user described a case where a former employee had copied product information from a company's website and used it for creating eBay offers. The user suspected a loss of the website's authority caused by the duplicate content.
In most cases this is not true, Mueller said. Normally when finding duplicate content, Google tries to identify the canoncial version and indexes this. Another possibility is that both pages are indexed. The reason is that not only the content itself but also other factors on a page are considered. In addition to this, the user's particular information need is incorporated. In the example, this can lead to a Person A with an affinity towards eBay who will see the eBay offer in the search results, whereas a Person B who is shown the product description stemming from the original website. This is determined by the respective context.
Summarised that means: Even if duplicate content from different domains is indexed by Google, this does not necessarily lead to inferior rankings. It merely means that some users will see the results of one page, whereas other users will see results of another page.
Subsequently you can find the video containing Mueller's explanation: