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Large reasoning models (LRMs) take longer on harder problems, just as humans do. This surface similarity hides an opposite pattern within items. When an LRM gets a problem wrong, it spends more tokens than when it gets the same problem right; humans do the reverse, spending less time on the trials they get wrong. We separate two levels of deliberation: how response time tracks difficulty across items (registration), and, with item identity held fixed, whether an agent spends more on its own failures or successes (allocation). On a public matched human-LRM corpus, humans and all five thinking LRMs reproduce the known cross-item alignment (registration) but diverge within items (allocation): every LRM shows a large wrong-vs-right effect (Cohen's d = 1.47-3.13 on H-ARC) while humans show the opposite sign. The comparison stays inside each agent's own scale; we never put seconds and tokens on one axis. The dissociation holds under item fixed effects, replicates across datasets, and is absent in a non-thinking baseline. We read the human pattern as engagement versus abandonment: people stay on items they expect to solve and give up on the rest. We read the LRM pattern as length driven by uncertainty: chains grow when the model is unsure, which is exactly when it tends to fail. Both policies produce the same cross-item correlation with difficulty, so they look aligned on the measure prior work has used; the divergence shows up only once item identity is fixed. Under resource-rational metareasoning, the split is between two stopping policies that share a difficulty signal but implement opposite control; trace length captures the signal and misses the control.