Modern codecs and with modern bandwidth these are becoming much less of an issue. Banding can be a problem at lower data rates. Yet, noise can result in less efficient encoding since encoders are designed to remove information that is similar from frame to frame to reduce size.
It’s not a conflict, it’s a juggle. You make the aesthetic decision by running test encodes. If vary by content and by distribution method. Vimeo and YouTube can deliver very high data rates so this is much less of an issue these days. If your source is good and you upload 720, 1080, UHD files and service recommended data rates, issues relating to banding or noise are much rarer. Since they’re going to crush whatever you give them, sometimes it’s hard to improve given their ultimate control.