I have used both and definitely prefer the bandsaw given the choice.
The dremel can work. I used a nonmetal Cut-Off Wheel (540, 420, 409). They're a thin quarter size. They work well for straight cuts, but if you bend them, they will break, which is one reason why the bandsaw is preferable. Cut curves around mouths all day long with the bandsaw. Straight cuts only with the dremel.
The bandsaw is also wet, where as the dremel obviously not, which I think can help to minimize damage around the cuts. Plus one can add a touch of iodine to the saw water, so the saw basically disinfects as it cuts, again minimizing damage, trauma and the likelihood of infection around the cuts.