Compression is going to change dynamics a lot more than normalizing. (Well, obviously, because that's what compression is intended to do). I'm not convinced there is actually a change in dynamics when you normalize, but there's definitely some aliasing, and the worst problem, as Juho pointed out, is the increased noise floor.
But I don't think the noise floor is raised any more than it is when you use makeup gain on a compressor, so the only advantage I'd see to compressing over normalizing is if there are actually dynamics that need to be subdued.
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