Now, "old" Saatchi is facing tough times. It has just announced significant staff cuts in its London office, after losing a host of clients. A week ago, pounds 1m of Procter and Gamble's media work was moved to a rival agency. In August, the lottery operator Camelot - Saatchi's flagship client - also left, as did the global Schweppes account.
Vision Express, after just three months as a Saatchi client, stalked off in July. And another key source of income, Visa, is currently reviewing whether to keep its account at Saatchi & Saatchi.
Most of the 20 redundancies at the Charlotte Street agency are administrative - essentially "wasteful processes", according to the agency.
On the plus side, Saatchi & Saatchi's performance was recently hailed by the City as the best for years. And new work has come in from Lloyds TSB, Guinness Africa and Rothmans.
But, overall, Saatchi & Saatchi clearly has its problems. It has substantially reshuffled the team responsible for bringing in new business, and taken the drastic step of importing creative expertise from overseas - not something that often happens in London agencies.
Meanwhile, at M&C Saatchi in Golden Square, all appears to be well. This month, for example, the company is busy with the launch of Sky Digital. The ad campaign, featuring TV sets pleading for a greater role in our lives, cost pounds 60m.
M&C has proved to be the greatest agency launch of all time, finding itself among the top 10 British agencies within just 18 months, with billings of around pounds 200m. In the first year, it humiliated "old Saatchi" by winning from it a number of major clients - Mirror, Gallaher, Dixons, British Airways. It also won some work from Mars, which had withdrawn its pounds 270m account in disgust from Saatchi & Saatchi.
Then there were Sekonda watches and PPP health care, Sainsbury's, Sears, the RAC and Bradford & Bingley. Oh, and the Conservative party. Maurice Saatchi had personally worked with the Tories since 1979. With the infamous "demon eyes" poster of Tony Blair, the agency earned pounds 13m from the Conservatives - equivalent to pounds 1.35 for every person who voted Tory, or pounds 170,000 for each seat the party won. By the beginning of this year, proving itself as politically adept as ever, M&C won from the Labour government a notable new task: promoting the Millennium Experience.
Increasingly, M&C is seen as beating "old" Saatchi and establishing itself definitively as the "real" Saatchi agency. Martin Jones, managing director of the Advertising Agency Register - an organisation that helps advertisers to choose a suitable agency - says: "people in the ad community think M&C has the mantle because it is doing the sort of things which made Saatchi famous... using power at high levels to get in and see clients. Everyone was envious of that in the Eighties, and they still are."
Talking of "old Saatchi", Moray MacLennan, joint managing director at M&C, admits that "there is a little frisson when you win against them". But Adam Crozier, joint managing director at Saatchi & Saatchi, says of "new" Saatchi: "we have pitched against them only once in four years. We are working in very different markets. We are a proven agency winning huge amounts of awards - far more than they are. We are on better pitch lists - not as many, perhaps, but we do not have as many gaps."
In the late Seventies and Eighties, the original Saatchi & Saatchi was impossible to ignore. Its slogan: Nothing is Impossible. Its ethos: be big, be flash. At one point in the headiest days, the agency was rumoured to be planning a bid to buy Midland Bank. And during a single year, according to Saatchi legend, Maurice alone spent more than pounds 40,000 on taxis and flowers. And the same ethos applied to the ads. Grandiose campaigns really did help transform the once-reviled British Airways into "the world's favourite airline". And print work such as the "Pregnant Man" poster and "Labour Isn't Working" for the Tories entered directly into advertising legend.
But the Saatchi spark is no longer there at "old Saatchi". In the first year after the split, it fell from the number one spot amongst agencies to sixth, but the following year showed an upturn. New work came in from Comet, Channel 5, Delta Airlines, Rothmans and Lloyds TSB.
The agency has lost oodles of UK business and relies substantially on international clients - which is bad for creativity because it's much harder to do memorable work for international clients than for domestic ones. Sure, there have been awards for some campaigns - for nurses, the Army and the Campaign for Racial Equality - but these are small budget campaigns. On the other hand, there's been a shameless BA rip-off for Delta Airlines, the current Norwich Union campaign featuring lots of singing folk in red braces, and an absolute howler for Visa Delta: Mel Smith dressed in a multicoloured boiler suit, shouting "Kerching".
M&C, despite its overall success, has had setbacks, too. It has been criticised for its poor creative work and for being responsible for the incomprehensible "tickle it you wrigglers" campaign for Fosters, and its work on BA does not bear comparison with the old campaigns.
The fates of the two Saatchi companies lead to one irresistible observation: if you were to merge them, you would have a super-agency, bigger and better than any other. Bigger and better, even, than the management could have dreamed of before the split.