Sculpting acts on vertices. These are either from the mesh itself (real geometry) or created with Multires modifier / dynamically with dyntopo. However in any case it uses geometry for painting with brushes because by painting you change position of certain vertices. Dyntopo in this case is kind of lazy way since it creates as many vertices as required for currently required level of details, subdividing / collapsing only part of mesh which is being worked on.
If geometry is uneven sculpting result won't be even as well in case of sculpting without dyntopo. Mesh in the file you attached is one of these examples:
This is wireframe of the mesh in question.
It won't act predictable being sculpted because proximity of horizontal edge loops is enough, while there are relatively small amount of vertical edge loops. When sculpted horizontal displacement will be detailed since there is plenty of geometry, but vertical will be lacking because there aren't as many vertical edge loops as horizontal ones. Since the sculpt will look stretched; inspite of the fact it has ~ 150 000 faces, it isn't really sculptable.
There are 2 general ways from here.
First, un-/subdivide edges of the mesh to get more or less even amount of edge loops in both directions (i.e. to get nearly squarish faces all over the mesh). In Edit mode either dissolve horizontal loop cuts (X > Dissolve Edges), or add more vertical loop cuts (Ctrl+R).
Second, enable dyntopo and set Subdivide Colalpse method of details with proper details size. Note that mesh will become triangulated.
Depending on the case both methods as always have their advantages and disadvantages; use the one which is faster for your situation.