What difference is there in reciting and listening to mantras? When reciting or listening to mantras such as Om Mani Pade Hum, what difference does it make when either listening, reciting or both?
The esoteric vibrations are what its all about. This is why the best mantras are in their original language (usually Sanskirt) not the transliterated and especially not the translated versions.

To answer your question: How much stronger would the vibrations be if you say it with your voice than your mind? Much much stronger. You are basically doing a magic summoning spell, summoning good karma and asking for the respective forces to help you. The more in-sync you are with the vibration the more likely they will be able to "hear"/feel your call and help you.

At higher stages of focus, where you are doing it mentally and you can ignore everything else, it does not make much of a difference because the focus is the same and the vibrations have already sufficiently transformed the body.

Thus, do it loudly verbally, using it as your focus.
Once your focus is developed (jhana) then you can do it silently.

I would recommend "How to mantra" by William Bodri for more esoteric information in regard to this subject.