Having recently watched both, I am here to tell you that Beverly Hills Cop holds up much better than Rain Man. I assume this is because Eddie Murphy's character is affable and amusing from the beginning, whereas Tom Cruise's character is all, "Where is my money? I deserve money! I have had a terrible life and it would be fixed by the money I so much deserve! I am so furious that I will yell at all other characters!" for about thee quarters of the movie. Also, Eddie Murphy's hair and, indeed, clothes, still look relatively normal, whereas Tom Cruise's are very "of the moment" for 1988, which, from the perspective of 2013, is not a positive thing.
Also, also: bananas in the tailpipe and later evocations of said bananas trump any number of toothpicks that Dustin Hoffman can instantly calculate.
That is all.