The prepositions in spite of and despite are exactly the same in all their definitions, and they are usually interchangeable. For writers who value brevity, despite is better. There’s nothing wrong with in spite of, though, and sometimes the three-syllable term sounds better than the two-syllable one.
Although despite generally appears about five times as often as in spite of, despite is even more heavily favored in edited writing. For example, the despite–in spite of ratio in large news publications like the New York Times and the Guardian is greater than 20 to one. One major exception is the British Financial Times, which uses despite only about twice as often as in spite of. We can’t explain this.
Again, there’s nothing wrong with in spite of in the following examples, but the shorter despite would work just as well:
In spite of this apparent failure of medical leadership, I believe there is yet time for an appropriate response. [Irish Times]
The fall in prices should accelerate in spite of the fact that the Memorial Day weekend is usually one of the biggest periods of the year for fuel demand. [LA Times]
In spite of that, Hydro said it managed to restore power to 43,000 customers within 24 hours. [CBC]