What are the differences and advantages of TensorFlow and Octave for machine learning?
Octave is a great language for prototyping and experimenting with ML algorithms, as it has built-in support for numerical linear algebra such as matrix and vector calculations. Octave is optimized for rapid calculations, which is very useful in Machine Learning. It is also quite easy to do matrix multiplications in Octave as Matrices are first-class objects in Octave. 

Tensorflow is indeed a versatile platform for machine learning with an ever-expanding list of packages and frameworks getting built. 

Octave is a good tool for learning the essentials and internals of mathematics of machine learning and Tensorflow is a good platform for building industry solutions for machine learning projects. Hence both are good for their own purposes.