Norton Op-Amps advantages
A norton opamp works with currents, you use one if you want to find the difference between two currents, then use a Norton operation amplifier. Even the Norton opamp outputs a voltage. 

Most applications and sensors don't use currents as a signal carrier. Using current usually means burning up power. One problem is many sensors are resistive and this also creates problems if you wanted to subtract currents to find the difference between them. I can't think of a reason to use a Norton op amp and subtract two currents (which is probably why you don't see them all that often), all of the examples in the link below show the Norton opamps being used to convert the Norton opamp to a voltage opamp. 


  The LM3900 is a 14-pin DIP containing four identical op-amps, each
  with inverting and noninverting inputs and an output. However, these
  op-amps are very different from the usual op-amp, and must be used in
  a completely different way. The usual op-amp responds to a
  differential voltage at its inputs, but the LM3900 responds to a
  differential current. Instead of a differential amplifier, the input
  stage is the current-differencing circuit shown at the right. The
  current mirror at the noninverting input subtracts the current at that
  input, I+, from the current at the inverting input, I-, to form the
  difference current I- - I+ that is furnished to the amplifier with
  overall gain of 70 dB. If I- is greater than I+, the output saturates
  low, and if I- is less, the output saturates high. Feedback from the
  output to the inverting input acts to reduce the difference current,
  which in normal operation is very small. This is just like the usual
  op-amp, except with current instead of voltage. The output, however,
  is a voltage as with the usual op-amp. The label "Norton" refers to
  the Norton equivalent circuit for a current source.


Source: https://mysite.du.edu/~etuttle/electron/elect21.htm