With Google the search is a lot smoother with the app and it gives me search suggestions. It's just optimal experience in my opinion.
Firefox doesn't have Bing as a default search option so I had to set it up manually - which then doesn't give me search suggestions either. Of course if I make my way to Bing.com it'll give me everything I want but it was way faster and easier to just click the dedicated Google search on the home page -- too bad the search is terrible like I said.
There's of course the chance I'm missing something like I said in op.