Also, if you have access to them, look at systems like WestLaw & Lexis and how they index information in various ways. Incorporating some of these ideas could be very helpful if made to the public - ie. the key system for indexing topics, history systems to see where ideas/articles are drawing their precedence from & how they have been used after publication.
They're run by very smart people who rely very heavily on algorithms and raw data and often ignore factors related to human needs and emotions. They do have their blind spots and weaknesses.
Despite Google's cries to the contrary, a lot of people don't trust them with private info. This is why DuckDuckGo's traffic is spiking. You can compete with Google on privacy.
Google's customer service is maybe the worst in the world. Even many paying customers get the big old middle finger when it comes to getting a problem resolved. That's a weakness that can be exploited.
Google has gotten much better at design in recent years by adopting a very minimalist and consistent style throughout their products, but you can still compete with them on design.