MOV is Apple's homebody: gorgeous on a Mac, awkward everywhere else. It was born in 1991, Apple's QuickTime team, and its real weak spot is traveling: Windows, Android and the web would all rather meet an MP4.
M4A is AAC in Apple's favorite outfit: the audio-only MP4 your iPhone speaks natively. An MP4 container holding only audio: usually AAC, occasionally Apple's lossless ALAC. That makes it the right destination when what you need is sounding great anywhere in the Apple ecosystem.