Something important has high significant, but something vital is absolutely necessary. Ex. Your arms and legs are very important, but your heart and brain are vital.

I would say that they mean the same thing. I think vital does stress importance more. It sounds a little more serious if vital is used rather than important. I think vital would be used to emphasise how there will be very negative consequences if something is not done.

vital means something very much necessary or essential to human life. Important means the need or the requirement for some purpose.