UTF-8 has an advantage in the case where ASCII characters represent the majority of characters in a block of text, because UTF-8 encodes these into 8 bits (like ASCII). It is also advantageous in that a UTF-8 file containing only ASCII characters has the same encoding as an ASCII file.
UTF-16 is better where ASCII is not predominant, since it uses 2 bytes per character, primarily. UTF-8 will start to use 3 or more bytes for the higher order characters where UTF-16 remains at just 2 bytes for most characters.
UTF-32 will cover all possible characters in 4 bytes. This makes it pretty bloated. I can’t think of any advantage to using it.