"They demonstrated a constructive way of dealing with differences," royal historian Robert Lacey told PEOPLE at Thursday's statue unveiling

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Prince William, Duke of Cambridge (L) and Britain's Prince Harry, Duke of Sussex chat ahead of the unveiling of a statue of their mother, Princess Diana
Credit: YUI MOK/POOL/AFP via Getty Images

Prince William and Prince Harry fundamentally understood the importance of setting aside their differences in paying public tribute to their late mother, Princess Diana.

"They demonstrated a constructive way of dealing with differences," royal historian Robert Lacey tells PEOPLE in the wake of Thursday's unveiling of a statue the brothers commissioned four years ago to honor their beloved mother.

"[They were] not sweeping [their differences] under the carpet but acknowledging more important things and doing that in a way that warmed everyone's heart," says Lacey, who has explored the tensions between William, 39, and Harry, 36, in his book Battle of Brothers.

Adds Ken Wharfe, who led the personal protection of Princess Diana and her sons for several years in the late '80s: "It was their idea and it was a joint effort."

The Duke of Cambridge and Duke of Sussex
Prince William and Prince Harry at the unveiling of a statue of their mother, Princess Diana, at Kensington Gardens.
| Credit: Alamy Stock Photo

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Lacey says the princes' restraint "illustrates their public style, both on their own and individually."

Despite speculation that William and Harry might each deliver a speech for the occasion, they ultimately issued a joint statement, saying in part: "Today, on what would have been our Mother's 60th birthday, we remember her love, strength and character — qualities that made her a force for good around the world, changing countless lives for the better. Every day, we wish she were still with us, and our hope is that this statue will be seen forever as a symbol of her life and her legacy."

The Duke of Cambridge and Duke of Sussex arrive for the unveiling of a statue they commissioned of their mother Diana, Princess of Wales
Prince William and Prince Harry unveil a statue of their mother, Princess Diana, at Kensington Gardens.
| Credit: Alamy Stock Photo

Says Lacey of the statement, "It was a very well-judged decision not to have speeches. The idea of rival speeches could have been disastrous, but to bring out a considered joint statement was perfect and shows a way ahead."