Does a denser wall produce a higher-energy barrier? And, if so, is there then actually a practical difference between the classical and quantum interpretations

Does a denser wall produce a higher-energy barrier? And, if so, is there then actually a practical difference between the classical and quantum interpretations? (i.e. could it simply be said that, the denser wall just has more chances to collide with the particle and stop it from passing through, thus explaining why the probability of finding it on the other side is lower?)