A container is only part of compatibility
MP4 and MOV can both contain audio and video, but the codecs and profiles inside determine whether a particular editor accepts them. Ask which video codec, audio format, frame rate, and profile the project expects. The .mov suffix alone is not a full editing specification.
Some workflows can rewrap compatible streams; others must transcode them. These operations affect quality differently. Inspect stream information and compare the result before using it in an edit. Keep the source MP4 and a camera master if one is available.