There are many complexities to this topic and some of them go back to the fundamentally differing definitions of probability employed by Bayesian statisticians versus frequentists. In practical terms ML and BI analyses using the same models of evolution often yield very very similar estimates of molecular phylogenies. The posterior probabilities (PP) on splits produced by BI are often quite different measures of support to bootstrap support (BS) that is typcially used for ML analysis. There is a growing literature as to why PP and BS differ so markedly. First of all, they are not measuring the same thing, so exact correspondence is not expected. Secondly, the PP of splits can be strongly affected by how well MCMC chains are mixing. This is an ongoing problem (getting good mixing of MCMC). Finally, it seems that Bayesian PPs are more sensitive to long branch attraction biases (see Susko (2008) Syst Biol. 57(4):602-12) in the absence of strong phylogenetic signal. However, BS values are also biased -- they are too low (see Susko (2009) Syst Biol. 58(2):211-23).

Often people prefer ML or BI merely because specific models of evolution are only available implemented in one or other framework. For example, Lartillot's CAT models are implemented in PHYLOBAYES and are not easily adaptable to ML (and the ML software hasn't been written).

A difficulty with datasets at 'low taxonomic levels' might be too few informative positions to generate much resolution in your tree. In this case you should be very very careful about Bayesian methods because they utilize prior probability distributions on all parameters -- if your data is not very informative, then the prior can have a rather large influence on the posterior distribution. This is not a problem unless you don't check what 'prior only' analyses look like.

Some people do cite philosophical reasons for the preference. For example, some Bayesians believe that hypotheses can have probabilities...hence you can put prior probability distributions on all parameters, including trees whereas a strict frequentist only allows probability distributions on random variables. Parameters should be estimated by maximizing the likelihood in this latter framework, not integrated over as in the Bayesian approach. Note that if the model is correct, then usually both ML and BI are statistically consistent -- so both will converge to the correct answer as the amount of data goes off to infinity.

BI is known to have poor resolution at lower taxonomic levels (species and below). The posterior probabilities are also known to higher than normal. While the answer to your question is going to depend on your question and focus of study, generally both methods do well but ML is very much accepted at all taxonomic levels. This does not mean that BI is invalid, it has been widely accepted and is a robust methodology.

In the absence of conclusive phylogenetic signal, low resolution may be appropriate: it's better to recover 'genuine' low resolution than to spuriously resolve polytomies.

You may to use some different methods and built the consensus tree as a result of your work. Also ML is widely used for such studies. What you mean under low-level taxonomy - specific or infraspecific? Also your results of each algorithm of tree constuction depend on lenth, quantity, quality and number of base chanches of your sequences.

There are many complexities to this topic and some of them go back to the fundamentally differing definitions of probability employed by Bayesian statisticians versus frequentists. In practical terms ML and BI analyses using the same models of evolution often yield very very similar estimates of molecular phylogenies. The posterior probabilities (PP) on splits produced by BI are often quite different measures of support to bootstrap support (BS) that is typcially used for ML analysis. There is a growing literature as to why PP and BS differ so markedly. First of all, they are not measuring the same thing, so exact correspondence is not expected. Secondly, the PP of splits can be strongly affected by how well MCMC chains are mixing. This is an ongoing problem (getting good mixing of MCMC). Finally, it seems that Bayesian PPs are more sensitive to long branch attraction biases (see Susko (2008) Syst Biol. 57(4):602-12) in the absence of strong phylogenetic signal. However, BS values are also biased -- they are too low (see Susko (2009) Syst Biol. 58(2):211-23).

Often people prefer ML or BI merely because specific models of evolution are only available implemented in one or other framework. For example, Lartillot's CAT models are implemented in PHYLOBAYES and are not easily adaptable to ML (and the ML software hasn't been written).

A difficulty with datasets at 'low taxonomic levels' might be too few informative positions to generate much resolution in your tree. In this case you should be very very careful about Bayesian methods because they utilize prior probability distributions on all parameters -- if your data is not very informative, then the prior can have a rather large influence on the posterior distribution. This is not a problem unless you don't check what 'prior only' analyses look like.

Some people do cite philosophical reasons for the preference. For example, some Bayesians believe that hypotheses can have probabilities...hence you can put prior probability distributions on all parameters, including trees whereas a strict frequentist only allows probability distributions on random variables. Parameters should be estimated by maximizing the likelihood in this latter framework, not integrated over as in the Bayesian approach. Note that if the model is correct, then usually both ML and BI are statistically consistent -- so both will converge to the correct answer as the amount of data goes off to infinity.

Setting aside the philosophical aspects, one of the big advantages of Bayesian methods is that they allow the use of more flexible and (very frequently) better-fitting, more realistic models of evolution. For example, and as Andrew mentioned, the CAT and CAT+GTR models are very general and widely applicable models that are only available in a Bayesian framework. One disadvantage is that they are usually slightly harder to use - you need to make sure MCMC chains converge. At the same time, ML methods usually use heuristics to find the best ML tree, and in principle should also be run multiple times to check whether the global optimum is being reached...how often people actually do that is unclear, I think.

One other point that is relevant here is the issue of model selection -- choice of the best fitting model of evolution. In the ML framework, for nested series of models model selection can most often be implemented through hierarchical series of likelihood ratio tests. For non-nested models, there are the information criteria (AIC, BIC etc). For Bayesian methods, model selection has proven more tricky because the widely used Bayes Factor criterion cannot be easily calculated for many models that one might wish to test amongst (e.g. CAT+GTR versus CAT+Poisson). Lartillot has proposed cross-validation as a model selection method and it seems to work well in practice, but this is only implemented in PHYLOBAYES. Posterior predictive siimulation is another avenue -- but suffers from many degrees of 'arbitrariness' (i.e. what measures does one use to assess model fit?). In practice this means that model selection is actually much more straightforward for ML than it is for BI.

I should note that there are some better implementations of Bayes factor calculations now available. For example, MrBayes now implements the 'stepping-stone' method of Xie et al. Syst Biol. (2011) 60(2):150-60 for nucleotide models in the GTR family. Furthremore, PHYLOBAYES uses 'thermodynamic integration' (path sampling) approaches for Bayes factor estimation for relaxed molecular clock models. I am unaware of any robust Bayes factor estimation methods for choosing amongst complex amino acid substitution models.

This overview might help. Basically, if you have enough data, you will get the same result using ML or Bayesian L or basic phylogenetics ("parsimony") - it's more about the quality and quantity of your data than the particular algorithm, because the algorithms differ in how they deal with putative homoplasy.