I was in both places for a week each a couple months ago. It rained a lot in Taveuni, and the rain was nearly constant in Beqa. It truly broke my spirit there. That was late May-early June. I was also in Beqa (in July) 22 years ago, and it rained every day then, too. I think the rainy season actually starts January 1 and ends December 31.
I thought the diving was great in Taveuni. The rain was mostly at night, and we had mostly sunny weather during the day. I loved the Great White Wall, etc. We stayed at Paradise Taveuni, and I thought it was one of the best resorts I have ever stayed at in my life. I was there with friends with whom I have dived in a number of places around the world, and our attitude has always been "too many places; too little time," so when we agreed that we would consider going back there rather than strike out for something new, that says something.
We did not like Beqa Lagoon Resort nearly as much for reasons I won't go into here. My biggest disappointment was the diving. I remembered the great bommies of 22 years ago, covered with coral and reef fish from bottom to top. Those are sad memories, because the coral on the bommies below 30-35 feet is mostly long dead, and the fish are long gone. My friends and I agreed that if we were to return to Fiji, it would not be there.