The effective control of start-up and power-up processes is essential if thermal power reactors are operated autonomously. The decision-making processes of an autonomous operating system must anticipate and suppress unwanted power fluctuations in a timely manner. The rapid and accurate predictions of the peak power to be expected in a surge can help an autonomous operating system to make more appropriate and timely decisions. This paper compares the predictive performance of the neural network with that of the decision tree, where both are based on peak power datasets for start-up and power-up processes. We explain how the datasets are constructed, i.e., by coupling the Monte Carlo sampling methods with the analysis of the system analysis procedure. We introduce a framework for the comprehensive evaluation of both prediction algorithms. We conclude that the neural network has better intrinsic predictive accuracy than the decision tree for the control of start-up and power-up processes. With further expansion of the datasets, it is expected that the predictive advantage of the neural network will become more evident. However, predictive accuracy is not the only criterion by which different predictive algorithms can be compared. The poor interpretability and high training costs of the neural network limit its application in practice while the accuracy of the decision tree can be improved via ensemble strategies. Therefore, deciding an algorithm to use is a complex selection process that should reflect the constraints of the specific application.