Are fgsea and Broad Institute GSEA equivalent? Several gene set enrichment methods are available, the most famous/popular is the Broad Institute tool. Many other tools are available (See for example the biocView of GSE which list 82 different packages). There are several parameters in consideration :


the statistic used to order the genes, 
if it competitive or self-contained,
if it is supervised or not,
and how is the enrichment score calculated.


I am using the fgsea - Fast Gene Set Enrichment Analysis package to calculate the enrichment scores and someone told me that the numbers are different from the ones on the Broad Institute despite all the other parameters being equivalent.

Are these two methods (fgsea and Broad Institute GSEA) equivalent to calculate the enrichment score?

I looked to the algorithms of both papers, and they seem fairly similar, but I don't know if in real datasets they are equivalent or not.

Is there any article reviewing and comparing how does the enrichment score method affect to the result?
According to the FGSEA preprint:


  We ran reference GSEA with default parameters. The permutation number
  was set to 1000, which means that for each input gene set 1000
  independent samples were generated. The run took 100 seconds and
  resulted in 79 gene sets with GSEA-adjusted FDR q-value of less than
  10−2. All significant gene sets were in a positive mode. First, to get
  a similar nominal p-values accuracy we ran FGSEA algorithm on 1000
  permutations. This took 2 seconds, but resulted in no significant hits
  due after multiple testing correction (with FRD ≤ 1%).


Thus, FGSEA and GSEA are not identical.

And again in the conclusion:


  Consequently, gene sets can be ranked more precisely in the results
  and, which is even more important, standard multiple testing
  correction methods can be applied instead of approximate ones as in
  [GSEA].


The author argues that FGSEA is more accurate, so it can't be equivalent.

If you are interested specifically in the enrichment score, that was addressed by the author in the preprint comments:


  Values of enrichment scores and normalized enrichment scores are the
  same for both broad version and fgsea.


So that part seems to be the same.