while dealing with Over Representation Analysis (ORA), there is drastic difference between the results given by WebGestalt and PANTHER. So, which one generate more reliable results for ORA analysis?
PANTHER uses a binomial test statistic (http://www.pantherdb.org/help/PANTHER_user_manual.pdf). This is not, strictly speaking, the correct test statistic (Fisher Exact Test would be correct), and this can create very different p-values for small sample sizes. For large samples, it will be approximately correct.