I think Shils painting surface, though perhaps similar to Auerbach in that the paint is applied thickly, is quite different.
I understand that Auerbach rarely does any sketches or preparation for his paintings -- particularly when painting figures, which he is known for. He just jumps right into the painting and his surfaces are almost sculptural....the paint is that thick.
I'm really not sure how Shils prepares his paintings....if he does sketches first, etc. however, it appears to me that his paint surface is not as "volatile" as Auerbach's. Shils' surfaces seem more evenly controlled and less sculptural and there is a lighter feeling to his paintings overall. Auerbach's feel heavy to me and since he's painting the figure more than Shils does, this may be appropriate whereas Shils may be going for a more atmospheric feeling given he paints predominately landscapes (or abstractions of landscapes.)
I have attached here an example of each --

Stuart Shils

Frank Auerbach