Neural Radiance Fields (NeRF) is an emerging 3D AI technology that generates 3D representations of objects or scenes from 2D images. This study investigates NeRF as a potential alternative to traditional photogrammetry for 3D reconstruction in the context of cultural heritage preservation. The research aims to discern the differences between these methods and assess NeRF's viability for the digital documentation of cultural heritage sites. The findings reveal that, when supplied with a complete dataset adhering to photogrammetry's capture methodology or a reduced-size dataset, NeRF demonstrates comparable, and at times superior, accuracy and completeness in point cloud reconstruction. NeRF excels in capturing complex scenes, including those with repetitive geometries, flat surfaces, reflective materials, and intricate patterns. However, NeRF faces challenges when further reducing the dataset's size, resulting in a significant drop in accuracy and an increase in noise compared to photogrammetry-generated models. Furthermore, NeRF demands more time, computing resources, and advanced software and computer programming skills from users. While NeRF does not currently replace photogrammetry, it complements it and presents potential benefits in heritage preservation. Its capacity to reconstruct from inconsistent datasets and handle challenging scenes underscores its significance in the field of historic preservation.