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The advantage to logical markup is that, regardless of how the affected text appears, it is always considered to be what the markup says it is. For example, a citation is always a citation, regardless of the font that any particular browser uses to represent it. The disadvantage to logical markup is that you cannot be sure how the text will appear (which may be important).
Conversely, the advantage to physical markup is that you can be sure of what the text will look like: when you want a typewriter font for a piece of text, you'll get typewriter font. The disadvantage to physical markup is that you may not be able to tell, just by looking at the font, what the text is supposed to represent (which may be important).
Do not feed the bears!