What's the similarities and differences between Wigner transform and wavelet transform?

There is a nice tutorial: Time-Frequency Toolbox For Use with MATLAB tthat compares many transformations, notably continuous wavelet transform and Wigner and its avatars.

Basically, the CWT belongs to atomic linear representations (a decomposition onto wavelet atoms), while Wigner-Ville is an energy distribution (to split the energy of signals over time and frequency).

Since the tutorial comes with a toolbox and many examples, you can easily reproduce it on your signals.