Welcome to ScubaBoard!
Both countries are beautiful and have a lot to offer.
As far as diving goes, I'd pick Fiji. It has those super colorful soft corals. The advantage of a liveaboard is that they can take you to areas with better visability. Some areas get much less rain than the others. Even if you stay on Beqa island and get some rain, there are still the shark dives. You could also stay in the northern part of Viti Levu (look up the Wananavu resort). This is where sugarcane is grown, it gets less rain.
Just as I loved the diving in Fiji, I also enjoyed the topside sites in Tahiti. I haven't visited Bora Bora yet, but I just returned from a week in Moorea. What spectacular scenery! My diving experience was mostly sharks, rays and small fish. There are lots of hard corals, but not the broccoli-like soft corals. If you were to travel to Rangiroa, I'm sure the sharks would be incredible.