Somebody else already outlined something similar but I found my problem to be a little different. When I open party chat in the beta there was a constant high pitch buzzing noise that would not stop. It was only the combination of Destiny Beta+ Party Chat. The chat voices were crystal clear but as soon as I unsnapped the chat our party could no longer hear each other. Using in-game chat was the only solution we found however the chat was lower quality this way, and just seemed all together worse i.e overly loud, a little crackly etc.
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They posted a fix for this about a day after the beta launched. You had to start your party and have all members join before anyone launched the beta. That fixed the party chat issue. As for the buzzing, that's the first I've ever heard of it.