Most likely you are looking at smooth shaded models. Smooth shading is a trick pulled by 3D graphics cards to make things look better without adding more polygons.
(The above smooth shading is actually not that pretty, there are ways to get even better shading)
Cura uses solid/flat shading, because that's how the model will print. As you can see, even on the smooth model, the edge of the model is not actually round.
Don't know what you mean by blocky. The only thing I can think of is that if these are 3d scans. 3d scans look real good because there is an image wrapped onto the model making it look much higher resolution than it actually is. When you remove the "skin" or image" you realize how crappy the scan actually is. Is that what you are talking about? If so then it's the scanner - they aren't as good as people make you think. If not then you need to show us a picture.
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