A better way to look at your equation, in my opinion, is
$$\Delta PE = -W_{\mathrm{cons}}.$$
That's closer to a definition of potential energy. But, in either order, another concept is that you can substitute a change in potential energy for the work by a conservative force when you analyze the motion of a system. In other words, you use either the work done by a conservative force or the potential energy contributions of that conservative interaction, but not both.
For example, in a system involving gravity and air resistance one could write (using $K$ for kinetic energy, $W$ for work, $U$ for potential energy)
$$K_{\mathrm{initial}}+W_{\mathrm{grav}}+W_{\mathrm{air}}=K_{\mathrm{final}}$$ using the work-energy principle, $$\Delta K = \Sigma_{\mathrm{all}} W.$$
Or$$K_{\mathrm{initial}}+U_{\mathrm{g,initial}}+W_{\mathrm{air}}=K_{\mathrm{final}}+U_{\mathrm{g,final}}.$$
You can see these are equivalent by subtracting $U_{\mathrm{g,final}}$ from both sides of the last equation and applying $\Delta U_{\mathrm{grav}}=-W_{\mathrm{grav}}$.
So the answer to your "or" question is neither of those is correct:
- Conservative forces can change kinetic energy and can be accounted either by the work they do or the change in potential energy of the system, and
- Non-conservative forces can change kinetic energy and must be accounted by the work they do. There isn't a potential energy function which helps us.
The work-energy theorem can be proven directly from Newton's 2nd law, without any reference to conservative or nonconservative forces.
The relations between conservtive forces and their potential energy (and in fact,
the existence of a scalar function satisfying these relations) is an entirely mathematical theorem. See here, here, and here.
After both of these results have been proven, one can separate the total work appearing in the work-energy theorem into the conservative and nonconservative parts. Since the conservative work is minus the difference in potential energy one can move it to the other side of the equation and get a positive difference in the total mechanical energy. In fact, the potential energy is defined so that the work equals the negative difference in the potential energy exactly because we want to get the difference in the mechanical energy (and not the difference in kinetic energy minus the difference in potential energy). That way, when the nonconservative forces do $0$ work we get conservation of energy.
Best Answer
Your question seems to arise from a problem in which there is both a conservative and a non-conservative force. When you say "PE" you must be referring to the PE of the conservative force (by definition there is no PE of a non-conservative force).
The work done by the conservative force does not depend on the path. Therefore you can define the potential as
$$\phi(x_0) - \phi(x) \equiv W_{x_0\to x}$$
Notice that: