This may be a little late to be of much use, but let me add a few thoughts regarding world cruises, focusing on Holland American and RSSC. I have been on part of an RSSC world cruise but not one on HA, although I have cruised on both lines.
First, if you are serious about a world cruise on one of those lines, you MUST take a short cruise on that line first. Aside from whether this might entitle you to some form of past passenger discount, the shorter cruise will help you with something far more important -- a chance to see whether you actually like the particular ship, its atmosphere, activities, food, the personnel, etc. No one cruise line is right for everyone and there is nothing worse than three months of being on the wrong ship at these prices.
Whether either of these is the right cruise line and right ship for you is very much a personal matter based on what each cruise line offers and what it is you specifically want from a cruise. A few thoughts.
These two cruise lines are notably different. RSSC places itself in the luxury market (although it is simply not on a par with Crystal, Seabourn, and Silverseas, the truly luxury lines, for a number of different reasons). HA is a notch below. Food will be somewhat better on RSSC but people will be more "down to earth" on HA. HA has a very loyal following and there are cruisers who have been going back for many years. RSSC has the larger and better-appointed staterooms (at least below the penthouse level). But, RSSC is somewhat "stuffier" and certainly more formal than HA. HA's passengers are, I believe, more diverse than those on RSSC. RSSC includes gratuities and alcohol in the cruise price; HA does not, but HA's prices are lower.
To look at these differences and see if the ship is right for you is why a short cruise is a good idea. But, be aware that a shorter cruise as a measuring rod has its drawbacks and will not give an accurate flavor of a longer cruise for at least two reasons. First, there will be far fewer port days per weeik on a world cruise than on a shorter cruise per week; you will have to entertain youselves on board rather than exploring onshore. Note that ships are very different on the days that they are in port compared to sea days. Therefore, before booking a world cruise, be VERY careful to review the activities and amenities offered by the line to see if they are to your liking - including lecturers, musical programs, entertainers, etc. An obvious example, if the line offers only big band music and more traditional ballroom stlyle dancing (foxtrot, waltz, etc.) and you do not like like either, you are out of luck. A good travel agent - one very familiar with both lines - is absolutely critical to this; do not rely on the promotional literature from the cruise line. The more specific information you can get, the better.
Second, the passenger profile on a world cruise is very different from the short cruises. World cruise passengers are significantly older than those on other cruises. I would estimate the average age at about 60 for most of RSSC's cruises and about 50 for HA. It is easily above 75-80 on the RSSC world cruise and, from what I have heard, above 65-70 on HA. (The longer the itinerary, the older the average passenger.) Passengers on a world cruise (at least those on the entire world cruise) are generraly retirees, with some well-heeled business people and mid to late career professionals thrown in. RSSC's passengers tend to come from the business and professional world; HA also has retired college professors, etc., that are not as abundant on RSSC. This profile will be very clearly reflected in the types of shows and performances put on, the lecturers and the subjects of their lectures, the music played in the lounges and for dancing, etc. To the extent that you want to participate in shipboard activities, make sure that you find out the activities that the ship offers and whether there are activities of interest to you. The activities, lecturers, shopping, etc., on each line will reflect the likes and wants of this clientele.
Be sure to look at those things that are of particular concern to you. If cabin size and comfort is primary (and a world cruise is a long time), then RSSC is probably preferable. If you are interested in shopping, RSSC's shops are more "high end" and "designer" with prices that are more high end as well. Of course, on board shopping is limited on both lines and prices tend to be on the high side. If you are primarily interested in food, then both lines have their strengths and weaknesses. Before my last RSSC cruise, I would have said that its food (including the whole dining experience) was better. But, on my several most recent RSSC cruises, I have experienced too many lapses for a luxury line, particularly in the main dining room (tasteless salmon, bickering waiters, waits for service, etc.). The alcohol included with dinner does not make up for these deficiencies. Similarly, I was not impressed with Voyager's specialty restaurant Signatures on my last cruise (a segment of a world cruise), probably because RSSC promised a truly gourmet experience but did not deliver. HA does not aspire to these same gournet levels of food and service. Thus, its lapses (and there have been some) did not appear as significant. It has good, generally well-prepared meals and the dining room has a less formal feeling. (If you are gourmands or are looking to treat yourselves to a really first-class dining exprience, you should look into Crystal, Seabourn, and Silversea. The food on each is definitely superior to RSSC and to HA.)
Select your cabin on the basis of the amount of time you plan to spend in it and your own personal need for space. Nothing worse than paying for the most expensive cabin on the ship and then using it only to sleep. Prabably, you would need at least the minimum penthouse because of space considerations and the amount you would take with you. (On RSSC Voyager, by the way, do not get a cabin aft of midships because Voyager has had a definite vibrarion problem in the aft part of the ship (and I am told it is worse at higher trans-oceanic speeds on the world cruise).
Finally, be sure to consider your own personal wants and needs. Several rather obvious examples: (1) If you like alcohol, RSSC provides wines with dinner (included in the cruise price) that are fairly good and it will be providing "open bar" elsewhere very soon. While you can avoid signing the chit for your drink (something I dislike about other lines), there does seem to be a certain percentage of people who go on RSSC because of the alcohol-included policy and who overdo it. (2) RSSC has open seating and single seating in its restaurants; HA has fixed seating with two different seatings. (3) Atmosphere - how formal or informal an on board atmosphere do you want? Do you want to dress up for dinner every night? How friendly do you want the crew? I have always sensed that HA is friendlier and somewhat less formal - both in terms of passengers and crew - and that RSSC is "stuffier" and more formal (of course, this is not a hard and fast rule).
Hope that some of this will be of help to you.