It's probably both. And I am cynical. A dead Diana nearly brought the RF down. the queen had to bow to Diana's passing coffin. No way they want a repeat of that and no way they should treat Kate the way they treated Diana.
They are being careful and controlling. As they should, if they don't want to repeat the mistakes of the past.
First, I don't agree that the Diana's death nearly brought down the Royal Family. There is an interesting review of the public opinion polls at that time in this article.
Ipsos MORI | Comment & Analysis | The Power of Public Opinion: Princess Diana: 1961-1997.
You may especially be interested in the response to a 1997 poll conducted September 4-5, a few days after Diana's death. In particular, review the questions about whether the country would be better or worse off without a monarchy or whether Charles would make a good King. At the height of the media attacks, there was a majority of people who thought Charles should step aside in favor of William, but he recovered 10 points within a month. Many U.S. politicians would give anything for approval ratings like that.
That said, I agree the royal family does not want a repeat of the Diana fiasco. But after more than 12 years, they know that Catherine is not Diana. They are trying to be more sensitive to her feelings than they were to Diana's, but it is certainly easier for them because Catherine is obviously not as volatile as Diana was.
I believe there are more likely reasons Catherine is not as visible as Diana. First, as Osipi said, they are in a different position within the royal family. William is not the Prince of Wales. But even if that wasn't true, I think the most important reason is that William and Catherine don't want her to be as visible as Diana was. I see absolutely nothing that indicates Catherine wants to make more official appearances. If anything, I think she would love to be able to go out without being stalked.
William hated the paparazzi and media attention even before Diana's death. By all accounts he loved serving in the military and preferred military service to appearing at public functions. There is absolutely no evidence that anything has changed.
I don't think it has much to do with Diana.