Hi Jenny. I share your frustration. Keep in mind that some of these databases are more current than other and they will have a different set of array probes and gene ontologies to test against.

With David, you submit a list of genes and the algo looks for enrichments in the ontologies that can be tested with Fisher exact or hypergeometric test. GO-elite is a bit more sophisticated and in addition to Fisher test performs permutations to see how often these enrichments are observed by chance. I would suggest that Go-Elite is a better approach, but I would also suggest to compare it with GSEA (preranked) as the "real" enrichments will be consistent for both methods.

For fun, try submitting a set of random genes to David a few times and get a feel for false positives.