In my example, the similarity did not require a hard proof but it was not seen for many years for the reasons which I would call "social".
In 1928 Weil (and simultaneously Siegel) defined and studied heights in algebraic number theory. In 1933 Henry Cartan introduced the Nevanlinna characteristic of a holomorphic curve in projective space. From certain view point these two things are the same:-)
In 1982 I noticed that these things are very much analogous, but I saw no application of this, and did not publish this observation. Probably many other people have noticed this too.
However in 1987, Paul Vojta pursued this analogy quite far. This became famous as Vojta's analogy, and many new results were proved inspired by this observation.
Why I called the reasons of this almost 60 years gap social? Because on my opinion the reason is that complex analists and algebraic geometers do not commnicate sufficiently with each other. In fact I told about my observation to a famous algebraic geometer in 1982. He was not excited. But when the news of the Vojta's analogy reached him few years later, he run into my office, and said: "Alex, can you quickly teach me Nevanlinna theory?"