I would like for a game engine to be able to have a lot of functions and easy and fast ways to create things like physics, collision, platformer module, shooting, steering, etc. that are very intuitive, and lots of templates. But within those very easy templates you always have the option to set advanced parameters and organize everything yourself.
So it allows for very fast game creation, and also the option to perfect and customize your game if you dive deeper.
That's what I would consider a great game engine.