Mr Watson, 49, whose current salary is £83,000, was appointed on Monday to the £73,000-a-year post of chief executive at Angus UA.
Mr Watson was not available for comment on his 12% pay cut but a spokesman for Tayside said the appointment to head Tayside from last Christmas had always been on an 'caretaker' basis.
Mr Watson's previous salary as Tayside director of education had been £72,192, said the spokesman. 'Looking at it purely in education terms, it's actually an increase', he said.
Midlothian UA, the first of the new unitaries to appoint a chief executive, last Wednesday chose Mr Muir (45). He has been Midlothian DC chief executive since 1987.
The £67,000 package of the new post was a rise of about £10,000 on his present package, said Mr Muir. 'It's a completely different job,' he said.
Mr Muir will do both jobs until the end of next March, with the new shadow authority funding only the pay increase.
- A second-tier officer has beaten 38 other applicants to win the job of chief executive of East Lothian UA. John Lindsay, currently director of finance and depute chief executive with the predecessor district council, will get an £17,000 pay rise to £65,000 a year. The current chief executive, Malcolm Duncan, had already announced his retirement.