Solvation effect on cyclohexane
The difference in behavior between the two methods is likely how much "wiggle" the molecule is allowed to have, or how much additional kinetic energy you allow the molecule to have when searching for the minimum energy conformation. The equatorial conformation is the global minimum conformation, but the axial conformation is a local minimum. Additionally, between the two conformations, there is another minimum called the twist-boat. You can read about them on this Wikipedia article or you could check out an introductory organic chemistry book from a library. Molecular dynamics tend to stop when a minimum is found. In other words, if a small alteration to the geometry increases the potential energy, the calculation stops. Monte Carlo calculations on molecules are designed to examine the evolution of conformation with time, and so geometry moves out of energy minima are allowed.  

Unsubstituted cyclohexane has four different conformations: Chair (relative energy 0 kJ/mol), half chair (+45 kJ/mol), twist boat (+23 kJ/mol), and boat (+30 kJ/mol). A molecular dynamics calculation may not allow large enough steps to get over the activation barrier to get out of a chair conformation. The following energy diagram shows the conformational space of cyclohexane.



The energy difference between equatorial and axial methylcyclohexane is 7.6 kJ/mol (1.6 kcal/mol on this table), which is small compared to the difference between the chair and the half-chair conformation. The energy diagram below approximates the energy steps between equatorial and axial methylcyclohexane.



Any computational method that allows potential energy steps large enough to get to the half-chair will certainly isomerize the axial conformer to the equatorial conformer. Presence or absence of solvent molecules in the simulation may be irrelevant.