My texture looks good on the rounded cylinder but poorly on the sphere

Hi

In Substance Designer you only need to concentrate on getting your material to look right on a tileable square. The various preview models are there to show what it might look like on different simple objects - but the spheres will always distort your texture.

Once you have your good tileable texture, applying it to a model is the role of Substance Painter where you can apply it to the surfaces using different projections.

There is an interim stage though, between the above, and that is the unwrapping of the model onto the UV surface.  This is usually done in your 3D modelling software, or in a dedicated application. It involves mapping the curves and shapes of the 3D model surface onto a flat surface (in a similar way in which a clothes designer lays out a flat pattern to cut out material).  On anything but the simplest model (e.g. a cube) this involves compromises in terms of where will you put seams, where can you allow a small degree of stretching and where can you not. This, in combination with Painters use of projection options, will be the key to applying your material succesfully and evenly to a model surface.

Dave