They have also come close to knocking lumps off one another in what has turned out to be one of the most effective, yet allegedly ill-humoured, relationships at the top of British business.
In September 1991, the company unveiled a slump in profits from pounds 376m to pounds 150m and launched a rescue rights issue to raise pounds 432m. The shares lost a quarter of their value in just a week.
At first, Mr Cahill's predecessor, Sir Roland Smith, planned merely to 'step back', leaving centre stage to Mr Evans, who had become chief executive the previous year.
But the big institutional shareholders would not wear that. They shunned the rights issue and demanded Sir Roland's head. This, despite the fact that he had masterminded the purchase of Rover in 1988 for what, even at the time, was recognised as enough of a steal to spark a storm around the head of Lord Young, the then Secretary of State for Trade and Industry.
By the autumn of 1991, however, that was history. A group of executive and non-executive directors, led by Mr Evans, informed Sir Roland that the BAe board had unanimously decided he must resign.
Canadian-born Sir Graham Day held the fort as stop-gap chairman, but it was an embarrassing seven months before Mr Cahill took over. It was a job few coveted; and Mr Cahill was even forced into denying it was a poisoned chalice.
He came with a formidable reputation as one of the four 'horsemen' who drove BTR to great heights during the 1960s and 1970s, along with Sir Owen Green, Norman Ireland and the late Don Tapley.
Mr Cahill needed all of that experience as BAe grappled with the combined problems of the UK recession and the worldwide defence downturn when peace broke out in Europe and the former USSR.
'Sales are fine,' he declared after spending a few months inspecting the group. 'We could even afford to shed a bit of sales, but we have got to get the company cash-positive, get costs down, and inevitably that means more jobs will go.' He was as good as his word: more than 50,000 jobs went. Mr Cahill cleared the decks, while he sent Mr Evans off round the world as BAe's super salesman.
Although both men went to minor boarding schools, their backgrounds are very different.
Mr Evans is a stocky Blackpudlian, the son of a civil engineer who died when he was a child. That was why he found himself at the Royal Masonic School in Hertfordshire. A motorcycle accident at the age of 16 meant plastic surgery and the end of his formal education.
Mr Evans began as a contracts officer at the Warton military aircraft factory in Lancashire. After a spell at Ferranti, he moved to British Aircraft Corporation - which eventually became a constituent of BAe - and specialised in selling to the Middle East.
Mr Cahill, 6 feet 4 inches tall, comes from an Irish Catholic family and admits he has had to learn to control a violent temper.
He had an unhappy time at school, sitting alone in his room in between regular beatings with the cane.
Like Mr Evans he left school at 16. But he learned an iron discipline: he hates unpunctuality and always pays bills as soon as they land.
Mr Cahill went straight into the City as a trainee stockbroker. However, this was the 1940s, when the Attlee government was at its height, and after two years he took fright at stories that the Stock Exchange would be nationalised.
So, he wrote 300 letters asking for a job. One went to the then Birmingham Tyre and Rubber Company, who made him the company's second post-war management trainee.
Towards the end of 1992, Mr Cahill was confident enough to predict that 1993 would herald 'a new beginning' for BAe. He was certainly right as far as the stock market was concerned: the shares did better than any other in the FT-SE 100 index last year.
Investors applauded a succession of disposals, including construction, computer services and the manufacture of corporate jets; and Mr Cahill made no secret of his wish to unload Rover.
With that done, BAe will be a concentrated defence company with a balance sheet containing manageable debts.
'Before this deal,' Mr Evans once declared, 'everything was a fire fight.'
The company still has its tantalising but frustrating Taiwan joint venture to tie up. But that now appears to be on ice until June.
As often happens in such cases, now that the worst is apparently past, the dynamic duo will have more spare time to take pot shots at one another.
Mr Evans has let it be known that he covets the chairmanship. What is more, stories have already surfaced that Mr Cahill may step down this year - even though his contract does not expire until April 1997 and he has insisted that he intends to see it out.
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