In a nutshell, the MOM is responsible for all things musical (the vocalists, band, songs, rehearsals, arrangements, etc...). The MOM should have the last say (other than the pastor). The MOM doesn't necessarily have to play and instrument.
Here's an ad for an MOM position that someone recently posted on this site; I kept it to help me examine myself:
Specific Responsibilities: (Music related)
• Provide opportunity for gifted musicians and artists to utilize their giftedness from a ministry platform
• Provide teaching for the church that challenges them in the area of personal as well as corporate worship so that they will be consistently encouraged to intentionally meet God
• Shepherd and disciple Worship Ministry members
• Prepare music for Sunday morning, Tuesday evening, and special events
• Conduct and rehearse vocal groups and instrumentalists
• Write arrangements for services, vocalists and instrumentalists
• Select music and orchestrations for vocalists and instrumentalists
• Audition singers and instrumentalists
Specific Responsibilities: (Non-music related)
• Help plan a yearly calendar and budget for the Worship Ministry and monitor expenditures, setting goals for growth
• Organize maintenance and repair of all music and sound equipment
• Arrange and coordinate use of music, sound, lighting personnel and equipment for services and special events
• Order new equipment
• Provide ministry data and reports as requested
Education
• Bachelor’s degree in music and/or Church Ministries preferred