Republicans would be more likely to win.
There are a lot more Republican that own guns (or at least used guns in the past) than Democrats. The Republicans would have more weapons, ammo, and gun experience at the beginning of the Civil War.
Many democrats would have to have guns supplied to them during the war. If guns and ammo were able to be supplied to most democrats, then they would still be at a disadvantage, due to the lack of gun experience. They would need to:
Get some target practice
Learn how to clean their guns
Practice reloading (reloading a gun is easier said than done)
Learn some safety rules so they don't accidentally friendly fire other Democrats
Yes, there are some Republicans without guns and gun experience, but not as many as Democrats.