There's only so many built-in and drop-in components available for the big engines; player movement, physics, render pipeline plumbing, UI frameworks, user settings, etc. You definitively do notice these things, if you care. It doesn't help that many devs (even AAA) keep bad defaults, so a huge chunk of Unreal games release with a comically-bad, laggy motion blur turned on.

Someone certainly could painstakingly replicate each badness of Unreal in Unity (and vice-versa), but until then, UE and Unity games often do feel like UE and Unity games. It's also rare to play a UE game that feels good and polished.