The primary benefit of a GPS over a paper map is that with a GPS you always know exactly where you are. With a paper map you only know exactly where you think you are. Now, just because you don't like where you are with the GPS doesn't make it any less accurate.
I use my iPhone as my GPS and I select satellite view so I can see exactly what is ahead rather than an abstract graphic representation of features. That way I don't end up on cart tracks.
As to accuracy of the two... You can get maps with a scale of 1:50,000 and 1:25,000 which is 1 inch to the mile and 2 inches to the mile that have every last twist and turn of every contour. Learn to read the contours and you get far more information than the normal GPS will give you - even with the satellite view. But if you want detail you can get GPS' that you can upload maps to and you can put the one and two inch to the mile maps on it. Then you get the benefit of the detail of the paper map without ever wondering where you are.
I have an old Garmin GPS 3+ that shows such features as Detroit and I-75 but after that information becomes a little sparse. Yet I use it every time we go hiking. Before we leave I turn it on, lock to the satellites and mark my location as 001 and turn it off... If I get lost then I'll turn it on and follow the little arrow back home, but I'll use my eyes and brain to decide how to get there when following the arrow. These stories of people driving into lakes and getting stuck in the woods are stories of people who simply didn't use their brains.