All else being equal, I would put more trust in the report that uses Bayesian statistics than a report that uses Frequentist statistics, but I wouldn't expect that strong an effect from that alone. (I would expect a strong increase in accuracy for using any kind of statistics over intuition.)

Following your link, I notice that Rasmussen's report used a fault tree. I would expect that the consideration of failure modes of each component of a nuclear reactor played a huge role in his accuracy, and that Bayesian and Frequentist statistics would largely agree how to get individual failure rates from historical data and how to synthesize this information into a failure rate for the whole reactor. Assuming the other experts did not also use fault trees, I would credit the fault trees more than Bayes for Rasmussen's success. (And if they did, I would wonder where they went wrong.)