Almost always, yes, it's better to get the independent travel insurance.
The only time I suggest anyone look at the insurance offered by the cruise line is if they're over 80 years old. The reason being is that the cruise line insurance is just based on length or cost of the cruise, whereas independent insurance is based on cost and age of the passenger. So the cruise line policy usually costs more for those who are younger, but cost less for those over 80. However, keep in mind that some of the cruise line insurance does not cover any airfare unless you book the air through them, plus sometimes their policy will only cover you for the length of the cruise and not the length of your travel (taking into account the day you leave your home and the day you return to your home). This is important if you're spending time before or after the cruise sightseeing or traveling. Many people going to far away places, like Europe or Asia, want to spend days or weeks traveling and the cruise is only a portion of their entire trip. Cruise line insurance would be a bad idea in this situation. Independent insurance will cover the air if you added that into the coverage amount and it will cover your entire trip, not just for the length of the cruise.
As you can see, deciding to purchase travel insurance is not as simple as yes or no. And what is right for one person or one trip may not be the right thing for another person or another trip. There are many things you have to take into consideration and this is why it's important to work with an agent so they can help with all the many details that go into the decision-making process.