Noise sensitivity of the (classical) Empirical Mode Decomposition routine
Indeed, at least in my experience, computing IMFs can be sensitive to borders, impulse signals and noise realizations.  As you are interested in wavelets, note that in Empirical mode decomposition as a filter bank a link is made with DWT:


  we report here on numerical experiments based on fractional Gaussian
  noise. In such a case, it turns out that EMD acts essentially as a
  dyadic filter bank resembling those involved in wavelet decompositions


Finally, there are regularized EMD schemes than apparently stabilize EMD decomposition, see for instance: A multicomponent proximal algorithm for empirical mode decomposition and related papers by this team.