By default NeRF does not produce a mesh (but one could use marching cubes as does Atlas) and it requires training a neural network for each scene whereas Atlas (as far as I understand it) uses pretrained network to process new scenes.

NeRF would probably produce a much better final result but the Atlas approach (no need to train something from scratch) is the only one that can hope to be run in real time which is vital for some application.