EMD is an adaptive technique. This has strengths but also weaknesses so whether you might use EMD vs MODWT depends a lot on your ultimate goal. The MODWT lends itself to robust statistical analysis because there is a lot known about the statistical properties of the wavelet coefficients, see for example MODWTVAR, MODWTXCORR for example. We are able to put confidence intervals around variance (power) estimates for the MODWT subbands precisely because we have good knowledge of the statistical behavior of the wavelet transform. That cannot be said for EMD. EMD is data adaptive.
I don't know which implementation of EMD, you are using, but there are at least four stopping criteria I know of for EMD algorithms. Depending on which you are using you may get a slightly different point at which the "sifting process" (as it is called) stops. Basically, it goes until it cannot generate any more (new) intrinsic mode functions -- how it determines that again depends on the algorithm you are using.
How far, the MODWT goes down is based on the sample size (and again with any wavelet transform, you don't have to go all the way). Bascially the MODWT will go down until what is left as the scaling coefficients is just equal to the mean of the signal. I'll demonstrate here:
wt = modwt(wecg);
Now look at
The above is essentially just a constant vector equal to the mean of the signal. Taking the wavelet transform any further is pointless, the wavelet coefficients will be nothing but zeros and the scaling coefficients won't change.
I think the differences in reconstruction you show above don't mean EMD is better than MODWT. These are very small differences. For example for my version of EMD,
imf = emd(wecg);
wt = modwt(wecg);
xrec = imodwt(wt);
imfrec = sum(imf);
So in the case of the EMD, the worst mismatch between the reconstruction and the signal sample is 10^(-16) for the MODWT (10^(-12)). Are we really worried about that difference? They both reconstruct the signal perfectly.
As far as the wavelet to choose, that depends on the goal of your analysis. What is your ultimate reason for doing a multiresolution analysis of these signals?