Each technique has its best use case: Euler Tour: Subtree queries (sum, min, updates on subtrees).
Simpler than HLD. Heavy-Light Decomposition: Path queries (sum on path, max on path).
Works with any path operation. Centroid Decomposition: Distance-related queries, counting pairs, nearest marked node. Best when paths through centroids matter.
Some problems need combinations. For example, path queries with subtree updates might use HLD for paths and Euler tour structure for subtrees.