The most important differences between Electrical Circuit and Magnetic Circuit are discussed in this article on the basis of Exciting Force, Current & Flux Density, Lines of Force, Series & Parallel Circuit Behavior, Insulation, Energy, Temperature, and Circuits Representation. The following table keys out the main Differences between Electric and Magnetic Circuit.
Difference between Electric and Magnetic Circuit
Characteristics  Electromotive force ( EMF) in volts  Magnetomotive force (MMF) in ampere turn 
Current / Flux  $Current=~~{}^{EMF}/{}_{Resistance}$  $Flux=~~{}^{MMF}/{}_{Reluctance}$ 
Resistance / Reluctance  $R=\rho \frac{L}{A}$
Where L is the length, ρ is resistivity, and A is the area.  $\Re =\frac{l}{\mu A}$
Where l is the length, μ is the permeability, and A is the area.

Current / Flux Density  Current Density (amp/area)
$\delta =\frac{I}{A}$  Flux Density ( Wb/area)
$B=\frac{\varphi }{A}$ 
Series Circuit  Current in all elements is same, but voltage or emf is different across each element.  Same flux passes through all elements in series and sum of MMF’s across the elements equal to applied MMF. 
Lines of Force  Electric lines of flux are not closed in an electric circuit.  Magnetic lines of flux are closed in a magnetic circuit. 
Parallel Circuit  Voltage across all branches is same and equal to applied voltage whereas current in the branches is different.  MMF of each branch is same and equal to the applied MMF. Flux in each branch is different and their sum equals the resultant flux. 
Insulation  Insulation confines the current to a definite path.  There is no perfect insulation for flux lines. It is impossible to confine all lines to the core path. 
Temperature  Resistance of an electric circuit changes with change in temperature.  The permeability and therefore reluctance of a magnetic materials vary over a wide range if temperature changes. 
Energy  Flow of an electric current in an electric circuit involves continuous dissipation of energy.  Energy is only needed for creating the flux initially and no energy is needed to maintain it. 
Insulating Materials  There are certain materials which act as an insulator and current cannot flow through them  Since there are no magnetic insulators so flux can pass through any material. 
Current / Flux Unit  Current is measured in Ampere (A).  Flux is measured in Weber (Wb). 
Conductance / Permeance  Conductance=1/Resistance  Permeance=1/Reluctance 
Electrons / Flux  In electric circuits, current flows (which is in fact the flow of electrons)  In magnetic circuits, flux sets up inside the magnetic circuit. 
Electric / Magnetic Lines of force  Electric lines start from a positive charge and terminate to a negative charge  Magnetic lines start from a North pole and terminate to a South pole. 
Representation   