Q.) What's the difference between Christmas and Bicycle Day.
A.) One perversely celebrates the origin of something that has destroyed countless people's ability to think and reason, whereas the other is Bicycle Day.
That joke just fails at even being terrible. The whole point of that joke structure is that you can misconstrue one thing for the other. e.g:
Q.) What's the difference between The Lord of the Rings and Atlas Shrugged.
A.) One is a childish fantasy that often engenders a lifelong obsession with its unbelievable heroes, leading to an emotionally stunted, socially crippled adulthood, unable to deal with the real world. The other, of course, involves orcs.
^ Structurally, also notice that the element order is reversed in the answer part compared to the question part. This is important, if you had asked it as
Q.) What's the difference between Bicycle Day and Christmas
A.) One perversely celebrates the origin of something that has destroyed countless people's ability to think and reason. The other, of course, involves bicycles.
It
actually works better. With your first version, I immediately was thinking "Christmas" for the answer. Putting bicycle day first makes it foremost in the mind. Also, break down the bicycle day thing in the answer too.