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Usually the websites and apps you use, but not what specific page you visit and it’s content.
If you for example visit https://en.wikipedia.org/wiki/Labor_unions_in_the_United_States they could see that you visited https://en.wikipedia.org/ but nothing more.
This is assuming that the website is encrypted (it starts with https://, not http://), which nowadays luckily most websites are. Otherwise they can see the specific page, it’s content and most likely also all information you input on that page.
I don’t think google fear Apple having to offer a choice to users. They fear Apple defaulting to Bing or something else.
While most people might choose google when presented with a choice, possibly more people are just going to keep the default settings when not presented with a choice.