Either one is Christian, so you're not considering changing your religion. Here are some basic differences.
Governance:
Southern Baptists (SB): Congregationalist organization. Churches call (hire) their own ministers. Although there is an over-arching organization, each congregation is autonomous.
United Methodists (UM): Episcopal (hierarchy with bishop) organization. Pastors are assigned by the bishop. Congregations are linked pretty tightly with one another.
Theology:
SB: Conservative, largely fundamentalist. Believe in adult baptism (not infant baptism), and always by full immersion. Evangelical approach to recruiting members. They believe that the Bible is infallible and is the sole basis for faith.
UM: Broader range of beliefs. Some fundamentalists, some liberals. All supposedly believe in the resurrection of Jesus. Some may not believe in the second coming. They allow infant baptism (christening) or adult baptism (either on the head or via full immersion). They consider faith based on the Bible, tradition, reason, and personal experience.
Social Action:
SB: Base their social actions primarily on saving souls, but there are several programs designed for improving the lives of others (hospitals, anti-poverty programs, etc.)
UM: Base their social programs more on improving the lives of others, with saving souls seen as important but not the first line of action. (They tend to think that someone has a hard time hearing the gospel when they're starving.)
Worship:
Almost indistinguishable, except when you see an adult baptism in a Baptist church. Most Baptist churches have a baptismal pool in the sanctuary.
Politics:
SB: Although they are risking a lot with the IRS, many SB churches have taken stands against abortion, gay marriage, and premarital sex. Oddly among Christians, they have been supportive of the war in Iraq and of military actions in general.
UM: Tend to focus on social justice issues somewhat more, although they also have taken stands against gay marriage. They tend to support programs that end poverty and promote education. They are against the Iraq war.
I hope this helps.