It is not that it does not work well, it is that you need to relearn to do a web search. Google's index is not that much superior, what is superior is their profiling engine, which is mainly design for their advertising networks but is used to adapts result to a user. So, if you do the same search in another search engine, just assume the search engine is a blank page and it does not know about your job, your habits and your preferences, so your search needs to be more precise.
Let's have a look at a glaring example. I am a software engineer. 7 years ago, I have started to ged rid of Google search engine. I tried a random search in DuckDuckGo. My first random search was "Opera". I assumed that the search engine would return results about the web browser, but 7 years ago, Opera browser was not popular at all, so the search engine returned results about the music genre opera, which totally makes sense. If I wanted to find stuff about the web browser Opera, I needed to search "browser opera". Nowadays, the Opera web browser fares better, and so, it is the first result when searched, so if you want to search about opera music, you need to be more specific and search "opera music".