I have two websites [url removed] and [url removed] with resembling content hosted on same server. Google pick only one of them. Is this a criteria of google to pick only one website from one server for identical content?
Google is doing their best to filter out duplicate content from their search results as it is low quality content and not what people a looking for. No matter where you host your sites this is going to happen. See the Panda Algortithm for more about this.