I have no idea if google is actually a better search engine, just that it's a familiar one.
(On Android you can't change it at all. And so I'm either stuck with a Google search on the Recents menu, or the "this widget could not be found" message)
If you're talking about at the Google Now or Siri then as far as I know that's not possible on either OS.
You only get either the bar, or an error message, which says the Google App can not be found.
It’s at the top since 5.0, can’t be removed, can’t be changed.
If you root and disable the Google App (yes, you now need root for that), then it is replaced with an error message, saying that the Google App could not be found.
There is no way to replace it with a search bar for bing, or remove it.