1. He preferred jazz to rock music.
2. He preferred jazz music to rock music.
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Does #1 mean #2? Is 'music' missing after 'jazz' in #1?
Since "jazz" obviously is music, the two sentences are the same. However, the redundancy in 2 makes 1 the better sentence.
Yes, they both mean the same thing. Jazz is a genre of music, so it need not be stated as in "jazz music" in relation to "rock music". Using the word "music" once is enough in this sentence, although it's fine to use it twice as in the second sentence.
Yes, #1 and #2 have the same meaning. In both sentences, the speaker is expressing a preference for jazz music over rock music. The phrase "to rock music" in #2 implies that the speaker is comparing jazz music specifically with rock music.
Regarding #1, it is not necessary to include the word "music" after "jazz" to convey the intended meaning. In this case, it is understood that the speaker is referring to music since the context of the sentence is comparing preferences in music genres.