As machine learning as a service continues gaining popularity, concerns about privacy and intellectual property arise. Users often hesitate to disclose their private information to obtain a service, while service providers aim to protect their proprietary models. Decision trees, a widely used machine learning model, are favoured for their simplicity, interpretability, and ease of training. In this context, Private Decision Tree Evaluation (PDTE) enables a server holding a private decision tree to provide predictions based on a client's private attributes. The protocol is such that the server learns nothing about the client's private attributes. Similarly, the client learns nothing about the server's model besides the prediction and some hyperparameters. In this paper, we propose two novel non-interactive PDTE protocols, XXCMP-PDTE and RCC-PDTE, based on two new non-interactive comparison protocols, XXCMP and RCC. Our evaluation of these comparison operators demonstrates that our proposed constructions can efficiently evaluate high-precision numbers. Specifically, RCC can compare 32-bit numbers in under 10 milliseconds. We assess our proposed PDTE protocols on decision trees trained over UCI datasets and compare our results with existing work in the field. Moreover, we evaluate synthetic decision trees to showcase scalability, revealing that RCC-PDTE can evaluate a decision tree with over 1000 nodes and 16 bits of precision in under 2 seconds. In contrast, the current state-of-the-art requires over 10 seconds to evaluate such a tree with only 11 bits of precision.