It depends on which codecs you’re working with.
If you’re editing in 10bit 4:2:2, that’s a YUV codec. In fact most normal editing codecs are YUV. The biggest normal exception would be HD 4:4:4 RGB. So if you render to it with AE, AE prepares the comp in RGB but then converts it to YUV to render to the codec.
FCP will automatically adjust whatever you put in the timeline to the native mode: so Animation codec (RGB) into a 10 bit 4:2:2 timeline will be rendered automatically to the YUV space. In my experience, it does a perfectly good job – there’s no noticeable shift in color.]
You might see gamma shifts though. There’s been a long outstanding problem with FCP and incorrect gamma interpretation. But that’s a whole new thread if you come across it.