We spent a week on the Paul Gauguin and absolutely loved it. Awesome way to see the various islands and of our 43 cruises is our all-time favorite - hands down the best ever!
Afterwards, we spent a week on a private island that was wonderful.
Both were extremely enjoyable for different reasons and I'm not sure I could decide between the two as to which one I liked the most, but if nailed to the wall, I'd have to lean more towards the cruise - just more to see and more to do.
As for which way to go, it's like Paul said, it really depends on your temperament and what you're more leaning towards.
Personally, while I really enjoyed the laid back relaxation of staying in the same place, I also really enjoyed visiting the various islands, trying different foods, seeing the various cultures, and hearing about all the history.
If you do decide to stay in one place, I would not recommend Tahiti. Instead, I would suggest looking at Bora Bora or Moorea. Keep in mind that getting to Moorea is cheaper (about $15 each way) and easier as there are ferries that make the short trip regularly during the day. Plus, the resorts are on the main island. There's also several places on the island to eat and/or shop. Whereas if you go to Bora Bora, you have to fly and the 45 minute flight will run about $450 per person roundtrip. There are very few places to eat and/or shop, but all the resorts are located on the motus surrounding the main island, so you have to take boats to and from the resorts.
But no matter what you decide to do, I know you will thoroughly love every minute of it - it's truly a magical place and it's as beautiful as any of the pictures you've ever seen.