Although it has been plagued with a string of mishaps, the cruise industry seems to be moving forward nicely. Carnival (CCL 0.43%) in particular was affected more than its competitors with the Costa Concordia accident as well as the "cruise from hell" on the Triumph, in addition to several other minor incidents. So now that peak vacation season is upon us, it seems like a good time to take another look and see how Carnival and the rest of the industry is moving forward.

The major players
Carnival is by far the largest of the publicly traded cruise lines, with a market cap about three times that of its nearest competitor, Royal Caribbean (RCL -0.26%). Carnival currently operates a fleet of 102 cruise ships under several brand names, including the Celebrity, Princess, and Seabourn lines, in addition to its flagship brand. Combined, the brands of Carnival control about half of the worldwide cruise market.

Royal Caribbean operates 41 ships under six different brand names, the best-known of which are Royal Caribbean and Celebrity Cruises. In recent years, Royal Caribbean has been best known for introducing the largest cruise ships in the world, its Oasis of the Seas and sister ship Allure of the Seas. The company plans to continue its trend of large ships with its upcoming "Quantum class" vessels, which are slightly smaller than the Oasis-class ships but are still among the largest in the industry.

The smallest and youngest (as a public company) is Norwegian Cruise Line (NCLH 0.83%). It has the youngest fleet of ships and has undertaken an impressive transformation of its image as well as an ambitious marketing campaign to boost public awareness of the company as a serious competitor. Norwegian also seems to be following the trend of larger ships, with a 4,200- passenger ship scheduled to be delivered in 2015, and possibly another one to follow.

Is demand coming back?
Carnival is expected to report a revenue decrease of around 2% for 2013 after a similar decline in 2012, mainly as a result of the recent incidents. However, the company has gone to great lengths to boost public confidence in cruises and to lure travelers back on board.

The company has revitalized some of its ships with amenities such as more dining options and more activities while on board. For example, Carnival has entered a partnership with celebrity chef Guy Fieri to create "Guy's Burger Joint" on some of its ships, as opposed to the standard hamburger option, as well as several other specialized dining choices.

In addition to revamping its existing fleet, Carnival plans to introduce at least two new ships per year through 2016, which will increase the company's capacity, although it is slower growth than has been seen over the past decade. The ultimate goal here is to create increased pricing power for Carnival (and the other cruise lines) by creating more demand than supply, which hasn't occurred in the cruise industry for several years.

The cruise lines as investments
The new ships and improvements of on-board amenities are expected to improve revenue and earnings, but just how much of an improvement is unknown at this point. Standard & Poor's expects a 4% increase in revenue per berth (per bed) for Carnival in 2014, which would reflect higher cabin prices as a result of higher demand.

Analysts disagree on whether or not Carnival and its rivals will be able to translate the higher revenues into higher profits. For example, of the 19 analysts who cover Carnival, earnings estimates for next year range from $1.24 to $2.00 per share, an extremely wide range. In other words, Carnival's shares could be trading anywhere from 17.7 to 28.5 times forward earnings, which makes valuing the company tough.

However, I think that Carnival is a pretty decent buy. The consensus calls for earnings of $2.20 per share the following year (with estimates ranging as high as $2.67), which is about 39% more than the midpoint on 2014's expectations. The only issue is that the competition simply looks like a better way to play it.

Royal Caribbean looks even better, with earnings growth of 34% and 24% expected for the next two years and a much narrower range of estimates. At the consensus, Royal Caribbean trades for just 13.8 times forward earnings, which is a fantastic price for the kind of earnings growth that is expected. Even though Carnival is revamping its fleet, Royal Caribbean is simply winning the race to offer the biggest and more feature-packed ships.

Norwegian, while the smallest and most speculative of the three, is expected to perform very well, with earnings expected to rise from an estimated $1.39 this year to $2.27 and $2.71 in 2014 and 2015, respectively. While it trades at the highest earnings multiple of the three, it has the most growth potential over the next few years.

So, what to do?
There are some great buys to be had in the cruise industry right now. While I feel that Carnival will be just fine in the long run, the other two companies simply offer a much better value. Royal Caribbean is the "safer," play but either way should provide very nice growth in the next few years.