In terms of raw power, Super Saiyajin Blue is more powerful. That’s because it is a more advanced version of the Super Saiyajin God form, just like Super Saiyajin 2 is a more advanced version of the basic Super Saiyajin form. The aren’t really any differences between the anime and the manga versions, though the manga has a lot more additional information about both forms. For example, the Super Saiyajin Blue form cannot be used at full power multiple times in a row. So if you use it a lot, it will be less powerful each time until you give it a rest for a while.