Selective routing is useful only when an expensive branch solves cases that a cheaper branch misses. We call this prerequisite expert complementarity and ask whether a capable iterative agent actually provides it. In a prospectively frozen financial question answering study, we compare Static with bounded ReAct across multiple capability tiers. Within each tier, the arms share the model, answer contract, retrieval interface, scoring, and resource limits. A stronger model removes ReAct’s average deficit and brings it to parity with Static, showing that relative performance depends on model choice. Yet Static and ReAct still succeed on nearly the same items. Across 150 shared items per tier, ReAct adds only one or two unique exact successes; oracle quality headroom point estimates are at most 1.7 points, while ReAct takes 2.1 to 2.6 times as long. A stability check preserves this pattern. Capability and complementarity are therefore distinct: improving an expensive branch can make it competitive without making it useful for routing. Evaluation contracts should be harmonized and paired complementarity audited before training a selector. This result concerns bounded ReAct over controlled benchmark evidence, not iterative agents in general.

Tool-using LLM agents are typically compared by accuracy alone, despite deployments being constrained by inference cost. We present a budgeted evaluation of common strategies for improving ReAct-style tool agents (multi-sample aggregation, iterative self-correction, and post-hoc answer revision) using Pareto analysis of cumulative accuracy versus token budget on three benchmarks (HotPotQA, FEVER, GSM8K) with Gemini 2.5 Flash. All experiments use three random seeds (N=500 per seed for HotPotQA/FEVER; N=1,015 for GSM8K); budgeted curves are computed post hoc from per-instance token logs. In our offline evaluation, Reflexion attains the highest accuracy on tool-heavy benchmarks (HotPotQA, FEVER), while CoT-SC leads on GSM8K. Reflexion’s reported token costs are optimistic lower bounds because retries are stopped using ground-truth feedback, and its accuracy is similarly optimistic: a deployment without access to ground-truth labels would not achieve the same accuracy because the gold-label stopping criterion would be unavailable; both costs and accuracy would differ in practice. Sampling-based approaches often spend 3-5x more tokens for comparatively small gains on tool-heavy tasks. GSM8K, a pure-math benchmark with minimal tool interaction, shows substantially larger gains for CoT-SC, TCAR, and Reflexion, larger than on tool-heavy benchmarks, though less sharply separated than headline accuracy alone would suggest, consistent with repeated tool trajectories being an important contributor to the observed efficiency gap in our tool-heavy settings. We provide a compute-aware evaluation protocol (frontier analysis and marginal-cost metrics) and practical guidance for choosing agent designs under different budget regimes.