keras vs. tensorflow.python.keras - which one to use?

Small update of 2019-10:

With the release of version 2.3.0, team Keras announced the following:

This is also the last major release of multi-backend Keras. Going forward, we recommend that users consider switching their Keras code to tf.keras in TensorFlow 2.0. It implements the same Keras 2.3.0 API (so switching should be as easy as changing the Keras import statements), but it has many advantages for TensorFlow users, such as support for eager execution, distribution, TPU training, and generally far better integration between low-level TensorFlow and high-level concepts like Layer and Model. It is also better maintained.

Development will focus on tf.keras going forward. We will keep maintaining multi-backend Keras over the next 6 months, but we will only be merging bug fixes. API changes will not be ported.

So by now, tf.keras seems to be the way to go.

tensorflow.python.keras is just a bundle of keras with a single backend inside tensorflow package. This allows you to start using keras by installing just pip install tensorflow.

keras package contains full keras library with three supported backends: tensorflow, theano and CNTK. If you even wish to switch between backends, you should choose keras package. This approach is also more flexible because it allows to install keras updates independently from tensorflow (which may not be easy to update, for example, because the next version may require a different version of CUDA driver) or vice versa. For this reason, I prefer to install keras as another package.

In terms of API, there is no difference right now, but keras will probably be integrated more tightly into tensorflow in the future. So there is a chance there will be tensorflow-only features in keras, but even in this case it's not a blocker to use keras package.

UPDATE

As of Keras 2.3.0 release, Francois Chollet announced that users should switch towards tf.keras instead of plain Keras. Therefore, the change to tf.keras instead of keras should be made by all users.