Recently I decided to learn MXNet, as some code I need to use, is written using this API.
However, I would like to know which are the advantages and disadvantages of MXNet compared to the other Deep Learning Libraries out there.
Perhaps the biggest reason for considering MXNet is its high-performance imperative API. This is one of the most important advantages of MXNet to other platforms. Imperative API with autograd makes it much easier and more intuitive to compose and debug a network. PyTorch also supports imperative API, but MXNet is the only platform AFAIK that supports hybridization, which effectively allows your imperative model to be converted to a symbol for similar performance to symbolic API. Here is a link to tutorials on Gluon, MXNet's imperative API: http://gluon.mxnet.io/
Given that you're using an example code, it is possible that the example was written using symbolic API. You may notice MXNet's advantage in symbolic API when training on many GPUs. Otherwise you won't notice much of a difference (except perhaps in some memory usage).
Tensorflow does have a one year head-start to MXNet and as a result it has a larger user base, but it only supports symbolic API (imperative API is very new and is only meant for experimentation), which is significantly harder to debug a network when you run into issues. However MXNet has quickly caught up in features and with 1.0 release, I don't think there is anything in TF that MXNet doesn't support.