If the extracted audio is heading into an editor rather than a music player, skip MP3 and take WAV. It's uncompressed 16-bit PCM: no lossy re-encode between the video's soundtrack and your timeline, and it drops straight into Audacity, Reaper, Premiere, Logic or any transcription tool without conversion prompts.
Do expect large files — roughly 10 MB per minute of stereo. Edit in WAV, then export to MP3 when you're ready to share.
When WAV beats MP3 for extracted audio
Any workflow that involves further processing benefits: noise reduction, levelling, compression, or splicing several recordings together. Each lossy encode compounds artefacts, so staying uncompressed until the final export keeps the result cleaner. Speech-to-text engines also tend to prefer WAV — many accept it natively and transcode anything else first.
What WAV won't do is improve on the source. If the MP4's audio was a modest 128 kbps AAC, the WAV is a faithful, very large copy of a 128 kbps recording.