Atomistic molecular dynamics simulations have been used to investigate differences in the characteristics of the aqueous solutions of two structurally similar, biologically important molecules, namely, tert-butyl alcohol (TBA) and trimethylamine- N-oxide (TMAO). By analyzing radial distribution functions, preferential solvation factors, and the number of nearest neighbors, structural characteristics of the two aqueous solutions are found to be dramatically different. By examining the distribution of nearest neighbor solute and solvent molecules in these two solutions, it is found that the aqueous solution of TMAO is homogeneous, whereas that of TBA is not. Further scrutiny of TBA-TBA radial distribution function at a high concentration by splitting the surrounding TBA molecules into two hemispheres demonstrates that the TBA aggregation occurs not only from the side of methyl moieties of TBA as expected in hydrophobicity-induced aggregation, but also from the side of the polar C-OH group. To analyze the effect of concentration of the two solute molecules (TBA and TMAO) on the local structure of water, tetrahedral order parameter and distributions of tetrahedral angles and hydrogen-bonding angles have been calculated for both the solutions. It is surprising to see that at high concentrations, the local water structure in the TMAO solution is more disrupted compared to the same in the TBA solution. Finally, the action of these two solutes on the folding-unfolding behavior of Trp-cage miniprotein has been analyzed and their contrasting activities toward the protein stability are correlated to the strikingly different behavior of their aqueous solutions.