Paths Versus Subtrees

Euler tour trees and link/cut trees both maintain a dynamic forest in $O(\log n)$ . What is the actual division of labor?

An ETT stores the Euler tour in a balanced BST, so it aggregates over subtrees and paths equally well, in worst case time. An LCT stores preferred paths, so it aggregates over the same two queries equally well, in amortized time.

An ETT stores the Euler tour in a balanced BST, so it aggregates over subtrees naturally and over paths badly. An LCT stores preferred paths, so it aggregates over paths naturally and over subtrees badly.

An ETT stores the Euler tour in a balanced BST, so it aggregates over paths naturally and over subtrees badly. An LCT stores preferred paths, so it aggregates over subtrees naturally and over paths badly.

An ETT stores the Euler tour of a general graph, so it aggregates over components naturally and over paths badly. An LCT stores preferred paths of a forest, so it aggregates over paths naturally and over subtrees badly.