It would help if you give some details like the budget, the size of group you have for your group. Luxury boats for Raja Empat can go from $4k-30k a day depending on what you want. Do you want a helipad? Phinisi vs steel hull? All these things have to be considered. Basically if you have the money you can get the boat of choice with the cruise director of choice anywhere in the world.
It's much more difficult to gauge "best" experiences because that is subjective. I usually pick the boat based on the knowledge of the crew before the luxuriousness of the boat. A few of my friends insist on certain luxuries without compromise. The more detail you give, the better advice can be given.
Budget isn't an issue - that may sound strange but I figure if you ask what the most luxurious liveaboards are you can't then quibble about cost. That said, if something is truly insane pricing out of whack with the value it brings I will consider that before going forward.
There are some enormous and very expensive yachts that are aimed mainly at charters to the billionaire yacht crowd. I am familiar with these, but they mostly do not have diving equipment, and even if they do they are not available in the best diving locations. Typically you can only find those in Med (with pathetic diving) or the Caribbean. There is good diving in the Caribbean, but mostly this can be accessed by land so there is less value to a liveaboard. So the giant charter yachts really don't count for the purpose of my question - I am asking for boats that are oriented to liveabord diving, located in fantastic diving locations.
You ask about a helipad, is that common on liveaboard dive boats? I assume this is a more hypothetical question. Helipads are found on some of the very large charter yachts, but I am not a fan of helicopters on boats. I have landed and taken off from boats with helipads a number of times. With really skilled people, and good conditions it can work, but not otherwise. Plus, the same family members that want the luxury are nervious about flying in helicopters, so this is not helpful.
Group size is flexible - probably 6 people minimum, but I assume that I could put together a set of say up 12 or so friends. We don't need the boat to be totally full either - some empty cabins and/or some single occupancy would be OK with us. Plus I may want some other guides along.
Knowledge of the crew is always important of course, particularly having great guides, and a competent captain.
In several parts of the world I have found guides to supplement the people on the boat. That takes up a cabin but can be worth it. For example, I have done this in the Galapagos - which is a liveaboard situation but it doesn't quite count as a prior experience since we weren't diving, just visting the islands (this was years ago, before I was certified). I found a boat to charter, then found a great biologist guide to supplement the local guide that came with the boat. In that case the two guides got along great and didn't have a power struggle etc., which can sometimes be an issue. I have done similar things with diving various places. Also with birding. Usually one can find guides who know an area would would love to be hired to go back. Of course if the boat already comes with great guides then that is fine.
However since some of my party are not super experienced divers I probably will hire some additional guides and/or some experienced divers no matter what so we have a higher ratio of guide to diver - more than most boats would normally do.
As to hull type - I am open. Having never been on a phinisi, I don't have much of an opinion one way or another.
Things that really matter to me, more or less in priority order are:
1. Safety. This probably goes without saying, but I will mention it. I have read postings about boats that (more than once) leave divers stranded in the water. I wouldn't want that. Of course nobody wants that, but some people can take it in stride. My family members include some nervious types that would find that really unacceptable. That includes safety on land too.
2. Power to charge batteries and run laptops to download photos. I assume pretty much every liveaboard has this.
3. Air conditioning - in lounge and cabin. This might not be requried some places due to climate, but we will want it in most warm water places.
4. Great food. Food can be local food (i.e. indonesian, thai, or other local ethnic cuisine would be great) but must be really good.
5. Adequate space is also nice - for gear, and just to avoid feeling cramped.
6. Stabilizers would add greatly to comfort while at sea. Rolling in rough seas is fine with me, it is almost impossible to get me sea sick, but alas the same is not true for some of my group. Stabilizers make a huge difference but they likely is not available for most liveaboard dive boats, unfortunately.
7. Internet connectivity. This would be great if it existed, but I assume that most places it doesn't.
8. Non diving activities have some value to me. It is possible that the group would include a non-diver or so, and if so then availability of snorkeling and/or some land based activites would be a plus if so. As an example, if I go to the Komodo area, I would definitely want to stop and see the dragons. I am a very serious topside wildlife photographer so that would be important. If I went to PNG / Irian Jaya I would want to do some land based birding and so forth. In most places the land based things would have to be before or after the liveaboard, but there are cases like Komodo where it would need to be integrated with the boat schedule.
9. Friendly crew and good service matters. Angry or diffident crew can negate just about any of the other factors. However, I suspect that most decent boats will have good crew.
10. Comfortable beds. This is subjective of course.
11. Hot tub, would be a great thing if available. Many yachts have them, and I think that some liveaboard dive boats do too, but it is not common. This is in the category of "nice to have", not a must have.
12. Decor is probably the least important "luxury" item. I don't care that much how a boat looks, inside or out. My picky family members will want it to be clean and hygenic. My guess is that most people who try to have a luxurious boat will have done something reasonable for decor. But I would be happy to dive from an ugly old tug boat if it had the other features above. A pretty boat that doesn't have the
13. It is nice when you can dive right off the boat, rather than having long tender rides. This is more a function of the locale than the boat of course.
14. Of course I want fantastic diving on top of all of this. There are obviously some trade offs with that - I am sure there are places that have great diving but are so-so in the luxury department. I would be fine with that, but I couldn't sell all my family members on that, which does not help domestic tranquility :-). Likelihood of good weather is also important.
That may not be all the details, but it ought to give you a better idea. It is possible that I have over constrained the problem, and that no boat has all of these features, so then it becomes an issue of some tradeoffs.
As an example in another area, I go to Africa to due topside wildlife photography, and there are safari camps and lodges that are set up to most the points above. Very few have air conditioning or internet, and of course this isn't a dive situation. However I have brought family groups to Africa very successfully. Even picky, luxury consious people can be happy deep in the bush in the middle of nowhere and see some amazing wild things - all because safari operators are set up to pander a bit to luxury. I want to replicate that sort of thing with a liveaboard dive boat.
Nathan
) and the Pelagian. The OR is a real dedicated dive boat with a rear dive deck. It was one of the best boats in Thailand in the late 90s.
) is a nice WA destination, and usually will have good viz. The Banda Sea is also a nice area although some of the old favorites have been trashed by fish bombers recently (Lucipara being one of those places tragically having walls stripped of coral by blast fishing). But we found some nice places this trip to go back to. The eastern greater sunda islands are all worth exploring, especially Komodo National Park. 
