Are you working in 23.98? 59.94i? 23.98 with a 3:2 pulldown to 59.94?
What is your source material? Are you bringing in 1080 video and working on it? Or creating original animation solely in AE?
What codec are you rendering to? ProRes? 10bit uncompressed? What are your sequence settings in AE? 1080 ProRes 23.98?
AE to FCP works great, but we need more info to help you!