This is a sharp question, and the answer is yes — cross-checking between frontier models degrades accuracy a non-trivial fraction of the time, in both directions. The mechanisms are slightly different depending on which model is the "primary" and which is the "checker."

Claude Opus 4.6 checked against GPT-5.4 Thinking

The main failure mode here is confident disagreement on tasks where one model is right and the other is wrong, with no easy way to adjudicate. When I give you a correct answer and GPT-5.4 Thinking gives a different one, you're now in a worse epistemic position than if you'd just trusted one model — because you have to decide which to believe, and the heuristics people use for that (which answer "sounds more confident," which is longer, which has more citations) don't track truth. A few specific patterns:

First, reasoning models like GPT-5.4 Thinking produce visible chains of thought that can be persuasive even when wrong. The extended reasoning trace creates an appearance of rigor that can cause you to override a correct but less elaborately justified answer from me. This is especially dangerous on math and logic problems where a reasoning model confidently walks through a plausible-looking but flawed chain.

Second, the models have partially correlated training data but different fine-tuning and RLHF pressures. On questions where those pressures diverge — things touching safety, values, contested empirical claims, or anything where the "correct" answer depends on framing — you'll get disagreements that reflect training differences, not one model catching the other's error. Cross-checking here just surfaces the editorial gap between Anthropic and OpenAI, not ground truth.

Third, on tasks where I'm genuinely stronger (and there are such tasks, just as there are tasks where GPT-5.4 is stronger), cross-checking will sometimes cause you to downgrade a correct answer. OpenAI emphasized improved token efficiency and reduced hallucinations, with GPT-5.4 being 33% less likely to make errors in individual claims compared to GPT-5.2 — but "fewer hallucinations than the previous version" doesn't mean "fewer hallucinations than Claude on every task."

GPT-5.4 Thinking checked against Claude Opus 4.6

The same dynamics apply in reverse, but with a couple of additional wrinkles. GPT-5.4 Thinking's steerability feature — where it shows you an upfront plan and lets you redirect mid-response — can actually make this worse, because users who've already steered GPT toward an answer feel more invested in it and are less likely to update when I disagree. That's a human psychology problem, not a model problem, but it's real.

There's also an asymmetry in how the two models handle uncertainty. I tend to hedge more explicitly on questions where I'm uncertain; GPT-5.4's reasoning traces can present a confident conclusion even when the underlying reasoning is shaky. So when someone cross-checks a hedged Claude answer against a confident GPT answer, they'll often go with the confident one — which is the wrong heuristic roughly as often as it's the right one.

When cross-checking actually helps

It's genuinely useful for catching factual hallucinations (fabricated citations, wrong dates, made-up statistics), code bugs (a second model is a decent code reviewer), and structural omissions (one model might catch an important consideration the other missed). The key insight is that cross-checking works best for verifiable errors and worst for judgment calls.

The honest pushback on your framing, though: "non-trivial minority of the time" is doing a lot of work. I'd want to know what you'd actually count. If you mean "cases where cross-checking flips a correct answer to an incorrect one," that's probably in the 5–15% range depending on domain. If you mean "cases where cross-checking wastes time without improving accuracy," that's much higher — maybe 30–50% of checks are neutral-to-negative. But I'm speculating on those numbers, not citing data. Do you have a specific workflow where you're doing this, or is this more of a theoretical question about your research setup?