Saatchis chiefs are said to be frustrated by the regularity with which Publicis has poached its leading creatives. A heated exchange is said to have occurred between Saatchis' creative chief, Tony Granger, and Dave Droga, Publicis' worldwide creative director, over the issue.
Droga ran Saatchis' London department until the end of last year and has worked with all of the teams that have now followed him to Publicis.
Robinson and Hillyard, who had been at Saatchis for 15 years, most recently as creative directors, are the fourth top-drawer creative team to leave Saatchis for roles with Publicis or its sister agency Fallon this year.
"Bob Isherwood (Saatchis' worldwide creative chief) and I have had discussions about this issue but we have a good relationship," Droga said.
In June, Nik Studzinski, Saatchis' head of art, took creative command of Publicis in London. He moved with his creative partner Gavin Kellett.
Howard Willmott and Duncan Marshall quit in April to become the executive creative directors of Publicis in New York.
In February, Fallon London hired Anthony Nelson and Mike Sutherland, the young team behind the successful Club 18-30 work, which won last year's Cannes Grand Prix.