I don't know the real reason at Bristol, but I would suggest that it was a straight financial decision.
I suspect that the majority of ATC staff and engineers at BRI were still in the old final salary pension scheme and also on terms and conditions transferred across from when Bristol was local authority run.
This would make the unit quite an expensive beast to run and although expensive in the short term, contracting out in the long term makes economic sense, especially if the radar task can be centralised and relieves the present owners of responsibility for a highly regulated department.
All of that applies to Woolsington and perhaps that's the way the owners at NCL see it.