Camera Moves or Player Moves for SideScroller

I'm making a infinite side scrolling game where I want to use 3D models for the characters because it is easier for me to create for animations. I would like to know the best way I can make the character move. Would it be to make the camera move vertically with the player attached to it? or Would it be to make the player move vertically? Can anyone help me with the movement this is the area I keep getting stuck on.