Binary Lifting vs Euler Tour

Binary lifting: $O(n \log n)$ preprocessing, $O(\log n)$ queries. Simple to implement and extend to weighted paths. Euler tour + RMQ: $O(n \log n)$ preprocessing, $O(1)$ queries. Faster for large $q$, but more complex and uses more space. For most problems, binary lifting is enough. The implementation is cleaner and easier to debug.

Use Euler tour + RMQ when $q > 10^6$ or when you need the absolute fastest queries. In competitive programming, binary lifting is the default choice. Only switch to Euler tour if you are certain the time limit requires $O(1)$ queries. The added complexity is not worth it for typical constraints.