The difference between cladistics and Linnean systematics is that the former rests on the axiomatic assumption that kinds are real, whereas the latter rests on the axiomatic assumption that kinds aren’t real (but our inventions).
The problem with cladistics is that it is inconsistent, actually ultimately paradoxically contradictory. Linnean systematics is consistent, but ultimately ambiguous.
These facts mean that biological systematics can just be either contradictory or ambiguous. The stage is thus set for an eternal battle in this discipline.