The most important difference is that the Southern Baptists are part of one of the largest organizations, the Southern Baptist Convention, and have an entire organizational ladder of authority that runs the denomination from the top down.
Non-denominational fellowships, as the name implies, are autonomous–each fellowship or church is entirely independent of any outside authority.
There are advantages and disadvantages to each model.
When a denomination is under the authority of a larger organization (convention, consistory, council, conference, governing board, etc.), that makes it harder for a pastor or a group of pastors to get involved with heretical teachings or questionable practices.
Also, if there are problems in the church, the members have a higher authority to appeal to; this is good especially when there is a crime (e.g. sexual abuse) or a continual sin by the pastor (e.g., sexual abuse), or a grievance (e.g., ill treatment of a church volunteer or staff member).
Another advantage of being part of a larger denomination is that in the event of financial difficulties, the denomination can step in and help keep the struggling church solvent for a while anyway.
Disadvantages include control of curricula (often the denomination will announce an “emphasis” e.g., “Strong Marriages” and every church in the denomination is required to order teaching material and outlines and do sermons, classes, etc. on this topic for a specified number of weeks of months, whether or not this topic is timely for the particular church. Pastors often feel stifled because they want to emphasize a topic that is more meaningful to their particular congregation, but they are not allowed to.
Another big disadvantage is that the denominational organization takes a percentage of the church offerings. (That’s how they have monies to distribute to needy congregations.) No one likes to have their money taken away!
A third disadvantage is that denominational churches must support the denominational missionaries and para-church organizations that they are told to support, and although they can add other missionaries to their budget, it’s difficult for them to provide financial support for other good missionaries and organizations. E.g., a parachurch organization that a lot of Protestants support is Campus Crusade for Christ; all the staff members of this organization must raise their own support. Sometimes a denominational church just can’t offer even their own people any sizeable support monies because the money is already earmarked for missionaries that the congregation doesn’t even know.
The advantages of the non-denominational churches are the opposite of the above. There is no controlling authority that tells the pastor and elders what to teach–if they decide they want to teach about racism or birth control or sins of the flesh or the doctrine of justifcation, or teach through a book of the Bible–they can do it! No higher authority will stop them.
Also non-denoms get to keep ALL their offerings and use them as they see fit. That means that they can build that youth center or coffeehouse or senior citizen home or give all the money to a motorcycle missionary or raise the pastor’s salary or hire a good professional praise band or…?!
But there are disadvantages. A non-denominational fellowship is on their own. If they go broke, no one will help them, and often, they will fold. Also, if their pastor leaves or gets ill, there is no denomination to provide them with an interim pastor.
The biggest problem with non-denominational churches is that there is no one to stop heretical teachings or un-Christian practices. This means that non-denominational churches are at great risk of falling into heresy, or even becoming cultish.
Many times, these churches are started by a dynamic pastor with a strong personality, and sometimes, these churches can become “cults of personality.” People attend mainly because of the pastor and his great sermons. When that pastor leaves, the church falls apart.
And of course, if there are any grievances, there is no recourse for the victims. In the event of an actual crime (e.g. sexual abuse), the victim can and should appeal to the secular law enforcement agencies and courts. But in the event of a spiritual abuse; e.g. being accused of sin and kicked out of your position in the church; there is no one for the victim to appeal to.
This is what happened to our family in a non-denominational church–we were kicked out because a woman pastor trumped up false charges against us. A tribunal was convened (we didn’t even know half the people in the tribunal, and they had never met us). It was frightening and horrific–I had nightmares for over a year, and still suffer a lot of anxiety and have major trust issues.
We tried to appeal to a higher authority in the church, but there wasn’t any. The pastor was the highest authority. So the matter has never been righted, and probably won’t be until Purgatory. I am personally grateful for the doctrine of Purgatory because it comforts me that these pastors and elders who mistreated our family WILL someday be held accountable for their sins and recompense WILL be required.