Computational burden of EMD/Huang-Hilbert vs wavelet
There are relationships between fixed wavelets and EMD, for certain classes of signals, cf. Empirical Mode Decompositions as data-driven wavelet-like wavelet-like expansions. A related relation between a fixed basis and an adaptive one can be found between Fourier transforms and Karhunen-Loève/PCA type decompositions.

Of course, when the vectors used for representations are learnt instead of being fixed beforehand, they are likely to require more computations. And are likely to be more difficult to implement online. Plus, DWT are often critically sampled, while EMD are redundant (hence greedier). Yet, some papers (see below) evaluate it proportionally to the burden of the FFT. Roughly to that of a redundant stationary wavelet transform.

Then, for non constrained versions, EMD can be quite sensitive to border effect, local spike instability, etc. As a result, from one signal to a similar other, a different number of IMFs can be necessary, which is not the case of a fixed-level DWT (but you can find that with adaptive wavelet packets).

Further, each can be sensitive to the features you can extract. 

So yes, it is not so surprising to me, with experience on seismic data and combustion signals with sporadic instabilities. Yet, it can work on some data.

Finally, some online implementations exist:


On-line empirical mode decomposition biomedical microprocessor for Hilbert Huang transform, 2011



  On-chip implementation of Hilbert-Huang transform (HHT) has great
  impact to analyze the non-linear and non-stationary biomedical signals
  on wearable or implantable sensors for the real-time applications.
  Empirical mode decomposition (EMD) is the key component for the HHT
  processor. In tradition, EMD is usually performed after the collection
  of a large window of signals, and the long latency may not be feasible
  for the real-time applications. In this work, the architecture of
  on-line EMD for biomedical signals is proposed. The on-line
  interpolation method with data reuse as well as component and
  iteration loop decomposition is applied to obtain low latency and low
  hardware cost. The first chip of EMD processor is fabricated in UMC
  90nm LL process and consumes 57.3µW.



Online Empirical Mode Decomposition, 2017



  The success of Empirical Mode Decomposition (EMD) resides in its
  practical approach to dissect non-stationary data. EMD repetitively
  goes through the entire data span to iteratively extract Intrinsic
  Mode Functions (IMFs). This approach, however, is not suitable for
  data stream as the entire data set has to be reconsidered every time a
  new point is added. To overcome this, we propose Online EMD, an
  algorithm that extracts IMFs on the fly. The two key elements of
  Online EMD are a sliding window to compute local IMFs, and a stitching
  procedure to gradually append local IMFs to the final result. Using
  synthetic data we show that the decomposition quality of Online EMD is
  similar to classical EMD. We also present results obtained with a real
  data set to expose the practical advantages of Online EMD when dealing
  with data stream or large data set.



On the computational complexity of the empirical mode decomposition algorithm, 2014



  It has been claimed that the empirical mode decomposition (EMD) and
  its improved version the ensemble EMD (EEMD) are computation
  intensive. In this study we will prove that the time complexity of the
  EMD/EEMD, which has never been analyzed before, is actually equivalent
  to that of the Fourier Transform. Numerical examples are presented to
  verify that EMD/EEMD is, in fact, a computationally efficient method.