If you have a brother or a sister you will be familiar with the concept of sibling rivalry.

It can be very divisive. For no apparent reason, children nurtured in the same womb have a tendency to fall out, sometimes temporarily, sometimes permanently, often spectacularly. The more trivial the argument, the greater the likelihood of long-term sibling acrimony.

My own sister and I have got round this problem brilliantly: we see each other once every five years. And I am always right.

But how hard it must be for two rather beautiful sisters who happen to live over the road from each other. They see each other every day. They have had millions of pounds lavished on their upbringing, their flamboyant lifestyles and their annual maintenance. Their parties are legendary, attracting movie icons, supermodels, pop stars and tycoons.

It must be hell because the question, rather inevitably, is: who is the prettiest sister?

Such is the dilemma facing The Dorchester and 45 Park Lane. It’s Mayfair’s grande dame versus the glamorous starlet.

The two hotels are part of the Dorchester Collection. When the group decided to open a younger, cooler hotel to complement the stately grandeur of The Dorchester, it could have stuck it in a different part of the capital, to avoid confusion.

But it didn’t. It built it alongside The Dorchester in the heart of Mayfair.

The spectacular project could have ended in tears, and in a sense it has – tears of joy.

I have stayed at The Dorchester a couple of times and was baffled by the concept of 45 Park Lane. Then I stayed there and suddenly it all made sense. The two sisters, who both have flawless skin and very warm hearts, get on so well because they are so different.

It’s all top hats, tails and English formality on the main entrance of The Dorchester. Roll up outside 45 and the tastefully tanned relaxed greeters are in black T-shirts and modern tailored jackets.

45 Park Lane has an active arts programme, including artist visits and exhibitions, and on the night I stayed over the wraps came off a temporary show by Chris Bracey and Christian Furr, devotees of the “art of electric miasma.” Think bright neon signs and reclaimed found objects.

Some of the works were displayed in the art deco-inspired Bar 45, where I was joined by my old friend Mr Purple who flies under the radar in the world of Whitehall politics.

As we worked our way through the bar’s tea-infused signature mixes – The Duke of Earl combines Earl Grey and Tanqueray gin with lemon and cane sugar syrup, which sounds awful but is moreish – Spandau Ballet’s Martin Kemp popped up to take a gander at a neon installation.

Mr Purple was so excited he leaned across the black granite bar and ordered a Forbidden Kiss from barman extraordinaire Thomas Morris. It was that kind of a night on the mezzanine level.

Now, I have always loved the front bar at The Dorchester, the one alongside Park Lane rather than the den at the back of The Promenade. But I rapidly fell under the spell of Bar 45. After three cocktails, I was eating out of its hands.

The big place over the road is home to one of the UK’s finest restaurants, the three Michelin-starred Alain Ducasse at The Dorchester, as well as the old-school Grill with its idiosyncratic tartan and traditional table service. Again, there has been no attempt to ape the formula.

Instead, 45 Park Lane is home to CUT, which is the mother of all modern, sleek steak restaurants, run by US big-hitter Wolfgang Puck.

There are USDA prime steaks and pure breed wagyu from Queensland, Australia. There is also an impressive selection of very fine American wines, reputedly the widest selection from Uncle Sam’s vineyards available in the UK.

Sadly, I had an evening engagement and couldn’t make dinner.

Later that night, I returned ready for bed. What a place to kick-back! The hotel is surprisingly small with only 45 bedrooms and suites, all with views of Hyde Park. The scale helps to reinforce the feeling of luxurious intimacy; the rooms are beautifully styled with original artwork, the latest digital widgetry and bags of neat design touches. Details do matter – and they are done very well at 45 Park Lane.

The bathroom offered up the sort of capacious comfort the jet set expect – black marble, deep sinks, tropical rain shower. Then it was just a case of slipping into the bed, which was about the size of a polo field, and hitting the button on the bedside computer that said: “Blinds.”

Goldfinger-style, the electronic blinds came down; Hyde Park disappeared; and it was time for 40 winks at 45.

FACTFILE

Richard McComb stayed at 45 Park Lane, London, W1K 1PN as a guest of The Dorchester Group.

Rates are from £523 per guest bedroom per night inclusive of breakfast and VAT, subject to availability.

Call 020 7493 4545 or visit www.45parklane.com