Are German tests really better than NHS ones?

No. Lyme disease tests used by official German laboratories are of the same type that the NHS uses, though they may be produced by a different manufacturer. Confusion arises because some private German laboratories use tests that have not been found to be helpful in diagnosis (eg EliSpot and LTT (Lymphocyte Transformation Test)) and also some which are not specific for Lyme disease, but can be abnormal in a range of other conditions (CD57+ immunological marker). See “Are other types of tests useful”