For univariate case time series forecast, I believe that this analyzes "statistical vs. machine learning models" depend on various factors. For example, the number of samples, the steps ahead, and the nature of the time series. Read the article that addresses one view of this discussion: https://arxiv.org/pdf/1909.13316.pdf.

About multivariate, I think that is the same idea as the univariate case.

You could start with this book: http://faculty.marshall.usc.edu/gareth-james/ISL/

I agree with Moisés Santos , it depends on the non-linearity of the dataset. Based on my exploration, statistical methods have overcome the ML methods for low non-linearity, but for high non-linearity, I found the ML methods its better than statistical methods.

I believe it's just a matter of time to achieve better ML results.

I agree with Moisés Santos: there are several factors affecting relative accuracy. Logically, we can expect that ML will produce better results for larger samples but standard statistical parametric methods will be better for small samples with good statistical properties.

Another issues here is the choice of the error measure used to compare alternative forecasting methods.

In this chapter we provide the following principles for choosing a good error metric:

Chapter Forecast Error Measures: Critical Review and Practical Recommendations

1) The optimisation criteria should match the evaluation criteria. As we explain on page 2, if we use a linear symmetric loss, then for a single series we optimize forecasts in terms of MAE.

2) And if we want to aggregate MAEs across series we need to use the geometric mean of relative MAEs, the AvgRelMAE measure.

At present I have not seen any good comparison conducted where the above two principles would be used. So this field of research remains not very much explored.