Actually, this question should never come up, as the uses of the two punctuation marks are quite different!
The colon is a very strong punctuation mark. It brings the reader to a dead stop! The only stronger punctuation mark is the period. You use a colon most often when you want to stop the reader before presenting a number of items in series.
Our reasons for choosing Hanover as a place of residence are these: the excellent school system, the weather, and the small town quality of life we experience here.
You can also use a colon for sheer emphasis:
When asked to name my favorite food, there is no contest: it’s popcorn.
The semicolon is also a very strong punctuation mark, but as I say, its functions are quite different. Its most useful function is to separate independent clauses (groups of words with subjects and predicates that could be sentences).
Her reasons for needing to go to the grocery were not major; she knew she could put the trip off till the next day.
The two clauses could each be sentences. For example–
Her reasons for needing to go to the grocery store were not major.
She knew she could put the trip off till the next day.
You would be perfectly correct in writing these thoughts this way. In determining to write the complete sentences or separate the two clauses with a semicolon, you simply ask how closely related the two ideas are. If it would be convenient for your reader to get the two thoughts “in the same breath,” then you would write one sentence, separating the two clauses with the semicolon. If you wanted to give each thought its own “weight,” then you’d write the two complete sentences.
Stay tuned! My next blog will cover an even more exciting way to use the semicolon!