Can you please give some more information about the alignment: how 'gappy' it is, how different the taxa are, what region/s of the genome are being analysed?

Also, both ML and Bayesian phylogenetic methods require a substitution model and potentially some information about distributions of rate categories. How are you deciding on these parameters?

From there, I can try to infer what might be going on.

First - check if you can graphically rearrange the tree. It is possible without loosing information about support of branches. 

Second - did you uuse the same substitution model and the same rate categories? It is important. Please, check it.

It is not surprizing at all. There can be several reason behind. As Agnieszka pointed out, you should double check the substitution parameters you used. For examle not all models are supported e.g in MrBayes which you can have in MEGA ML. Also there can be only orientational differences in the tree you got. If it so rearranging the tree you can have the very same topologies.  And third, you can have different topologies because the phylogenetic signal of your gene(s) used  is ot strong enought. In this case the weakly supported clades can appear differently using different methods.

As mentioned prior, please provide more detail on the differences between the topologies using Baysian and ML methods. To add to the above suggested reasons behind topological differences: MrBayes draws poorly supported nodes as polytomies while ML (in MEGA) will draw splits even with poor bootstrap support. Furthermore, I suggest you use  Figtree or Mesquite to explore orientational differences.

Yes, FigTree (http://tree.bio.ed.ac.uk/software/figtree/) is really brilliant for manipulating trees.

Thank you all for your valuable suggestions and time.

I have used 16S mitochondrial gene sequences of different species of same genus and used GTR +G+I substitution model. I have used fig tree to interpret output from mr bayes.