My (subjective and objective) findings between WaveNet and LSTM is:
WaveNet - Pros
Achieves good frequency response even in extreme cases like EQs
Manages to model some ambience
Easy to train
WaveNet - Cons
Unbearable higher frequencies that becomes more prominent the more distortion the model has. Sounds like aliasing and in the end all high gain amplifiers/pedals/etc sound about the same.
Post-ringing
CPU usage
LSTM - Pros
Distortion sounds very good and no audible aliasing like sounds.
No post-ringing
Low CPU
LSTM - Cons
Does not achieve very good frequency response with extreme EQing like WaveNet does
Loses some higher frequencies at lower quality BUT is solved by increasing mostly hidden size but also increases CPU usage
Option to incorporate a convolutional layer in front of LSTM models. Helps w/ sensitivity to delay, and generally improves training.