MusicBee is a music manager/player built for Windows first and foremost, AIFF is an Apple format that is comparable to WAV. It's basically an extremely-limited, Apple-wrapped PCM format. As far as I know, AIFF is not open-source and therefore Steven probably runs into many issues for supporting that format in MusicBee.
Converting to a universally-supported format such as WAV, and more preferably a compressed format such as FLAC with support for Vorbis comments, is by far the preferred choice for handling files. You will get more compatibility and way more functionality in regards to tagging, since AIFF is extremely limited in what it can actually write. It truly is a terrible format that has been largely unsupported for years outside of Mac-based products.
Preferred formats that are universal overall...
Uncompressed lossless - WAV (not worth it since lossless is the exact same final output but smaller in size)
Compressed lossless - FLAC
Compressed lossy - MP3 or AAC
There are other formats, but these are by far the most common.