It may be more useful to begin first by distinguishing the two denominations’ similarities before discussing their differences. Both denominations agree on the following items, which are absolutely essential to be considered an orthodox Christian: The Deity of Jesus Christ, the fall of mankind and Original Sin, the Canon of Scripture and its authority in the life of the believer, the doctrine of the Trinity, the Incarnation of Christ, the new birth of the believer, and the final judgment of sin and wickedness. With these things in place, both denominations are squarely within the realm of orthodoxy.
However, there are certainly differences between the two. Local autonomy of Baptist congregations is one. The Baptist denomination supports the freedom of the local church, and as such, are not controlled by the denomination, persay. In the Church of God, you have a defined leadership structure outside of the churches, much like the United Methodists. Another difference is in the area of spiritual gifts. While the Church of God emphasizes spiritual gifts today, including prophecy and speaking in tongues, they are of diminished importance, and in some cases taught as having ceased after the first century in Baptist churches. Another difference is in the area of baptism. For Baptists, infant baptism is not permitted, as each believer must make the choice to be baptized. In the Church of God, infant baptism is allowed. Another difference is in end times views. Baptist churches tend to not emphasize any certain view of eschatology, the doctrinal statements of the Church of God specifically state their support for a pre-tribulational rapture and Jesus’ return to earth for a 1,000 year reign as king before the final eternal state. Another difference between the two denominations is that Baptists trace their routes from the Anabaptist movement, whereas the Church of God can trace its history to the Wesleyan/Arminian tradition of the 1700s. It is out of these two diverse historical backgrounds that their differences can be understood to arise out of.
Both denominations have produced quite a number of contributions to our current theology in America, and both denominations have some solid viewpoints. As with all things, it is best to take what we get from any denomination or church body and examine it in light of our final authority on earth, the written Word of God.