Stamford Hospital has been given a clean bill of health by inspectors who praised patient care across all departments.
But Peterborough City Hospital, which is run by the same trust, has been told it needs to improve.
The Care Quality Commission inspected both hospitals in March this year.
The results were published this week, with Stamford Hospital getting a good rating for its accident and emergency, surgery, the outpatients departments and medical care.
Inspectors said they all demonstrated “consistently good care” for patients.
But the £289 million Peterborough City Hospital, which faces an annual deficit of £40 million, was given a requiring improvement grade. Six out of eight service areas were rated good, but inspectors found failings in child protection, complaints systems and pain relief for terminally ill patients.
Areas of good practice across both hospitals, including a “joint school” for hip or knee surgery patients, were praised in the inspectors’ report.
Director of care quality and chief nurse at Peterborough and Stamford Hospitals Trust Chris Wilkinson said work was being done to improve problem areas.
“Prior to the inspection, work had already begun on a detailed action plan picking up areas noted where improvements should be made,” he added.
“The medical and emergency departments present the greatest challenges for our trust, as they are consistently under pressure from a growing number of older and more unwell patients.
“To combat this, we are actively recruiting to nursing and medical posts, and to managerial roles, to support these departments further.”
Mr Wilkinson said work was also being done with other health and social care partners on the processes around discharging patients.