For the British royal family last week's birth was an unalloyed success.

Not only did Prince George, third in line to the throne, come into this world safely and with the minimum of fuss but the royal brand was given a huge boost.

The birth dominated the headlines for most of the week, stirring feverish speculation about every detail from the child's name to his mother's post-birth slimming regime. Coming on top of last year's hugely successful diamond jubilee celebrations and the feel-good factor created by the Olympic Games, this has been another triumph for perception over reality.

Not so long ago, the pavements outside Buckingham Palace were packed with supermarket bouquets and angry crowds demanding the Queen show some compassion for her recently deceased daughter-in-law, Princess Diana. Forget the fire at Windsor Castle in 1992 and the steady breakdown of her children's marriages, the real annus horribilis for the Queen came five years later when she and her family were subjected to public obloquy following the untimely death of the so-called "People's Princess" (thank you, Tony Blair).

In purely public relations terms, things had to get better and they did. One of the first turning points was the sight of Princess Diana's two sons, Prince William and Prince Harry, walking behind the funeral cortege with their father, grandfather and uncle. In his diaries, Labour's spin doctor Alastair Campbell claimed there was initial reluctance but the fact remains that few people could have been left unmoved by that poignant image.

An uneasy truce was then declared with the media over coverage of the two young princes who were growing up. Largely it held and the Queen's own standing was helped by an unprecedented broadcast in which she appeared to apologise for failings in the handling of her daughter-in-law's death. By the time of her diamond jubilee last year, a MORI poll indicated that her approval ratings had soared to 90%.

In the last 20 years, much has been done to burnish that image and as a result the standing of the royal family has prospered.

It has also been helped by decisions which would have been unthinkable in the past such as opening the Queen's finances to greater public scrutiny, to pay income tax and to open the royal palaces to the public.

Her visit to Dublin in 2011 was the first to the Irish Republic by a British monarch; it was a great success which not only passed without incident, but was instrumental in continuing the healing process for half a century of violence and bitter recrimination.

The decision to allow the Prince of Wales to marry Camilla Parker-Bowles was also seen as a good thing and underlined the truth of the conservative adage that things have to change if they are to remain the same.

All told, the Queen and the royal family are in a much happier place than they were two decades ago when it seemed as if they might be torn apart by their own shortcomings – the unhappy marriages, the scandals, the inherited wealth, the absurd protocol and the widely-held perception that they accepted power without responsibility.

Cynics say the change has come about by a PR process which has simply reinvented the monarchy for the next generation.

While there is some truth in that allegation – the royal family website reveals a slick operation – there is also a sense that members of "the Firm" (as King George VI once called his family) have learned to move with the times and to appear more relaxed. Just look at the difference between the new fathers now and then. Last week, Prince William appeared outside St Mary's Hospital in casual trousers and sleeves rolled up as if accepting the new challenge. In 1982, Prince Charles stood in the same place wearing a tie and a pin-striped suit as if he was judging a baby show.

Behind the glow of wellbeing, though, one matter remains unspoken: the succession. At present the Queen is 87 and given her general state of health, she could live to be 100.

If so, she will still be on the throne, as according to Prime Minister David Cameron, the suggestion she might abdicate is "out of the question". That would mean that her son and heir Prince Charles would be 78 and Prince William would be in his mid-40s.

Compare all this to what has been happening in the other European monarchies and a rather different picture emerges. Last weekend, King Albert I of Belgium, aged 79, abdicated in favour of his son Philippe after 20 years on the throne and the skies did not fall in.

The ceremony was met with polite indifference and the leader of the republican N-VA party Jan Jambon said that the event left him "cold ... it just passes me by".

Last year saw a similar abdication when Queen Beatrix of the Netherlands, aged 75, stood aside and handed the throne to her son Crown Prince Willem-Alexander. There was no coronation and very little ceremony and the new Dutch king – the first since 1890 – swore himself in before the Dutch people calling them not "subjects" but "citizens". The only people wearing crowns were those donning orange inflatable models for fun, while the real crown rested on a table in front of the new king.

It was all very understated but the Netherlands have a constitutional monarchy which remains reasonably popular. Not that Willem-Alexander was always so squeaky clean. As a young man the Crown Prince was a party animal who was lampooned as "Prince Pils" and he attracted further criticism when he announced his engagement to Máxima Zorreguieta, the daughter of a leading member of the Argentine junta.

Even so, those failings (such as they were) pale in comparison to some of the accusations that have been levelled at Britain's younger royals, perhaps because Europe's media is less dazzled by European royalty and their behaviour.

Only in Spain has there been a downturn. It was bad enough when King Juan Carlos was photographed earlier this year on an elephant hunt in Botswana but things got worse when it was revealed that his companion was not his wife.

At a time when the country was facing an economic crisis with 25% of the workforce on the dole, this did not look good and the press had a field day.

Scandals have also nibbled at the reputations of the Norwegian and Swedish royal families, where surveys show that respect for them is at an all-time low due to the usual revelations of sex, dodgy deals and abuse of privilege. Only Denmark remains unscathed. A constitutional amendment brought Queen Margethe II to the throne in 1972 as the first female monarch and she is deservedly popular, as is her son Prince Frederick, who married Australian marketing consultant Mary Donaldson in 2003. Their son, Prince Christian, is the first member of the Danish royal family to attend a state school.

After collecting his son from hospital, Prince William proved his self-reliance by fixing the baby chair in his car and jumping into the driving seat. A hands-on dad, a prince with the common touch ... a myth that somehow seduces a nation.