The history of TDE and backup compression is that until SQL 2016, they were great features that didn’t play well together – if TDE was in play, backup compression didn’t work well, or at all.
However, with the release of SQL 2016, Microsoft aimed to have these two awesome features get along better (the blog post announcing this feature interoperability is here). Then there was this “you need to patch” post, due to edge cases that might cause your backup to not be restored. So if you haven’t patched in a while, now would be a good time to do so, because Microsoft says those issues have been resolved (although that seems to be disputed here).
My sympathies definitely lie toward backup compression over TDE if forced to choose between the two.