The OpenSearch keyword search defaults to OR. There's no support for AND or + operators in the search syntax.
Search behaviour is consistent across local and remote repositories - they're all using the same search back-end. So, I'm not sure why you're getting inconsistent results.
A freemarker template is used to build the keyword search query - it's in config/alfresco/templates/api/KeywordSearch_query_.ftl. It could be changed to use AND instead of OR.
In 2.1, I hope we can support the same syntax as the Web Client search.