Adenine and cytosine methylation are two important epigenetic modifications of DNA sequences at the levels of the genome and transcriptome. To characterize the differential roles of methylating adenine or cytosine with respect to their hydration properties, we performed conventional MD simulations and free energy perturbation calculations for two particular DNA sequences, namely the brain-derived neurotrophic factor (BDNF) promoter and the R.DpnI-bound DNA that are known to undergo methylation of C5-methyl cytosine and N6-methyl adenine, respectively. We found that a single methylated cytosine has a clearly favorable hydration free energy over cytosine since the attached methyl group has a slightly polar character. In contrast, capping the strongly polar N6 of adenine with a methyl group gives a slightly unfavorable contribution to its free energy of solvation. Performing the same demethylation in the context of a DNA double-strand gave quite similar results for the more solvent-accessible cytosine but much more unfavorable results for the rather buried adenine. Interestingly, the same demethylation reactions are far more unfavorable when performed in the context of the opposite (BDNF or R.DpnI target) sequence. This suggests a natural preference for methylation in a specific sequence context. In addition, free energy calculations for demethylating adenine or cytosine in the context of B-DNA vs. Z-DNA suggest that the conformational B-Z transition of DNA transition is rather a property of cytosine methylated sequences but is not preferable for the adenine-methylated sequences investigated here.