"Does one type of string contribute to more vibration/handshock than the other?"
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In general, you will get less "vibration/handshock" with a "Fastflite" type low stretch string. So the answer to your question is yes. Many people still like the feel of a dacron string, however, you'll find that the majority, myself included, would rather shoot "fastflite."
While others may disagree, I've taken many an older bow, reinforced the tips for low stretch strings, and it immediately had a more "pleasant" feel on release and shot with more authority.