That's a really hard question, as Google "Search" is more like a personal assistant than just a search engine. But I guess there is one feature which makes me ditch Google again and again: SECURITY.
The problem with Google (or rather the whole of Alphabet) is that it is too big with too many different personal products. It stores data, it connects data and it finds out stuff about you which I think is too personal. All in the pursuit of better UX. Don't get me wrong, I trust Alphabet. They use my private data to improve their products, not to sell it. But I do not want just some company (not even Google) to know me better than my very own family. There are bad people and organizations everywhere, especially the state which wants to know everything about all the people from everywhere in the world - and there are laws even Google has to abide. That's why I use proxy search engines, like Disconnect.me or DuckDuckGo; in desperate search of something better for me and the rest of the world >.>