I think it depends on whether the answer is verifiable.
I have tested two judge models in my apps:
1. Judge model for a resume tailor. It evaluated the result resume vs the base resume and JD and judged it out of 10 on fit and honesty. It worked well and was useful.
2. Review model in my LLM trading bot platform. It reviews decisions from the Main model. The problem here is that the bot is navigating ambiguity. So unless the Review model catches an outright blunder (e.g. making a decision on wrong candle price or a BUY when it should be a SELL), the Review model can do more harm than good.
First, it adds latency to decisions, decisions take twice the amount of time (like be 60s instead of 30s for Gemma 4 31B). Second, it can make the bot too cautious, because Review model only runs on BUY/SELL decisions and not HOLD decisions, so the bot will only make less trades instead of review model increasing number of trades (because of latency and cost).
So overall, I think you'll get better results with a better model single shotting it rather than a review model if the answer isn't easily verifiable. But then why do you need a judge model and not just have the same agent review itself?
ALSO, if you read the reasoning text for a reasoning model (like Gemma 4), you see that it ALREADY reviews itself. So it's doing its best, re-review isn't really adding information. It's an interesting experiment, but you need to evaluate on a case by case basis.