DFS and BFS embody opposite information strategies. Each step of a depth-first search commits to one branch, harvesting maximal information about that path before retreating; the algorithm is greedy for path-knowledge and accepts the risk of ending up in a region that turns out not to contain the answer. Each step of a breadth-first search refuses to commit, expanding the frontier uniformly and keeping all options live; entropy stays high until evidence forces a decision.
This explains why the two strategies are optimal for different objectives. DFS finds some solution as quickly as possible because it follows whichever branch of the local information landscape looks promising; backtracking is the algorithmic version of unlearning when a path turns out wrong. BFS finds the globally optimal solution in unweighted graphs because uniform expansion guarantees that the first time the target is touched is along the shortest path. Each level of BFS is an iso-distance set, equal information content with respect to the source.
The trade-off generalizes well outside graph search. Exploitation versus exploration is the same shape: DFS-style commitment maximizes return on what you currently believe; BFS-style hedging preserves optionality when the cost of being wrong is high. Resource allocation, learning strategies, and risk management all surface the same dichotomy. Deep specialization (DFS) compounds returns on a chosen direction; broad foundation (BFS) keeps all moves available until the right one is forced. See DFS and BFS Are Complementary Search Strategies for the implementation-level companion, and Graph Search Is O(V+E)-Optimal for why neither pays an asymptotic premium for its strategy.