When reading through the phylogenetic literature, a split may be observed between those who favour maximum likelihood and those who consider Bayesian methods superior. Of course, a number of paper used mixed methods, but usual there is a tendency to either side.
Having seen that in Geneious now PhyML has several options, I looked up the PhyML website for some details. The options with which you can run PhyML are a) the well-known bootstrap, b) the approximate likelihood test (aLRT), c) aLRT with parametric branch support using Chi2, d) aLRT non-parametric branch support based on Shimodaira-Hasegawa-like procedure. See http://www.atgc-montpellier.fr/phyml/alrt/ for more details. There is also data on a benchmark comparing the options:
Interesting enough, in their paper describing the aLRT statistic, Anisimova & Gascuel (2006) present a figure which clearly shows the comparison with simulated data sets. This allows for a theoretical ‘fair-play’.
Although I am applying different methods on the same empirical data set, I always had the impression that the Bayesian method as implemented in BEAST. I feel a little more confident now, but one should always be open for the ‘Popperian black swans’. Science is all about skepticism…
Anisimova, M. & Gascuel, O., 2006. Approximate likelihood ratio test for branches: a fast, accurate and powerful alternative. – Systematic Biology 55: 539-552.