I think a new engine could rival Google, but how do you define "better than."

As bballad illustrates, different people have different opinions or ideas of what they want their searches to return. Based solely on what the top 10 sites returned for your search are one search engine may be "better" than another because their search algorithm may fit more with your way of thinking.

That said, if you delve another level down on Google and use the Advanced Search there is nothing you can't find. You can search for keywords, or specify keywords that CAN'T be in the results. You can search on a specific phrase. You can look for results only in a certain language, of a certain file type, a specific date range, or limit your search to only one domain.

You can use it as a tool to find out who is linked to a site (I use it to find out who is linked to my sites) by doing a search on results that are linked to a specific URL. You can also perform some topic-specific searches.

Other search engines may offer similar granularity, but I doubt there is anything you can't find on the Internet if you know how to use the Google advanced search properly.

For more info I recommend checking out this tutorial: Unraveling Google