What is the best way to enlarge or shrink a shape drawn using the shape tool;
By pressing CTRL T and resizing
By using the direct path selection tool and dragging selected anchor points?
Is there a noteworthy difference? If so, what?
It ultimately doesn't matter with Shape Layers or Vector Layers in Photoshop. No method is definitively better than the other.
The difference between Transforming and the Direct Selection Tool is the ability to alter anchor placement. Transform can be easier if you just want to alter an entire shape. However, the Direct Selection Tool is almost required if you want to simply adjust one path segment or curve of a shape.