I listen to radio stations all the time and can tell you that there is no problem with MusicBee there. With the same DSP settings, I usually have to INCREASE the volume for local mp3's. Many stations are quieter because of the level they are being transmitted at by the source compared to other stations who crank up the DB.
What DSPs are you using? Any kind of compressor/limiter/normalization? What are your output settings (wasapi, DS, etc)? How are you controlling your volume? In your Windows volume mixer, check where MusicBee is at.
Also, please ensure you have updated to the latest 3.3x version of MusicBee.