Thank you John, I will test those and will come back with some results.
One problem with webp is that I could not open the files in some web browsers. As I wish to serve these tiles on the web, I need them to open in most of the web browsers. This is probably the most important part, that I forgot to mention.
As you said, serving two formats is a good option. I decided today to continue tests with png and jp2. I will try to see if jpeg xr is a viable solution.
I also noticed that the output of the png files is PNG32. I should be able to maybe reduce those as well (their size), especially on the tiles that have many pixels of the same color.
Raiz Roland Robert