In neomenthyl chloride, the leaving group (Cl-) is attached to a secondary carbon, while in menthyl chloride, the leaving group is attached to a tertiary carbon. In general, secondary carbocations are more stable than tertiary carbocations. This is because the positive charge of a secondary carbocation is spread out over three carbon atoms, while the positive charge of a tertiary carbocation is concentrated on one carbon atom. The more stable the carbocation, the faster the elimination reaction will occur.

Another factor that contributes to the faster elimination rate of neomenthyl chloride is the steric hindrance around the reaction center. In neomenthyl chloride, the leaving group is less hindered than in menthyl chloride. This means that the leaving group can leave more easily in neomenthyl chloride, which results in a faster elimination reaction.

Finally, the solvent can also play a role in the rate of elimination reactions. In general, polar solvents favor substitution reactions, while nonpolar solvents favor elimination reactions. In the case of neomenthyl chloride and menthyl chloride, the solvent is usually a mixture of polar and nonpolar solvents. The nonpolar solvent helps to promote the elimination reaction, while the polar solvent helps to suppress the substitution reaction.

Overall, the combination of factors mentioned above results in neomenthyl chloride undergoing elimination faster than menthyl chloride.