Your sample data doesn't make sense, but here is my closest guess, you should be able to figure what you want if this isn't exactly it.
DECLARE @Part1 TABLE
(DHBService varchar(10),
PU varchar(10),
Budget decimal(10,2),
Admission varchar(10))
INSERT @Part1
SELECT 'ABC', 'M00', 200, 'Acute' UNION ALL
SELECT 'ADC', 'M10', 300, 'Severe'
DECLARE @Part2 TABLE
(DHBService varchar(10),
PU varchar(10),
Admission varchar(10),
Actuals decimal(10,2))
INSERT @Part2
SELECT 'ABC', 'M10', 'Severe', 412.88 UNION ALL
SELECT 'ADD', 'M12', 'Acute', 333
SELECT coalesce(P1.DHBService, P2.DHBService) AS DHBService,
coalesce(P1.PU, P2.PU) AS PU,
coalesce(P1.Admission, P2.Admission) AS Admission,
P1.Budget, P2.Actuals
FROM @Part1 P1
FULL JOIN @Part2 P2 ON P1.DHBService = P2.DHBService AND P1.PU = P2.PU AND P1.Admission = P2.Admission