More power will flow, in fact substantially more since power goes at the square of voltage. This doesn't say what will happen when said power flows. Depending on the atty, it could finally get cooking for the first time, hit the sweet spot perfectly, go past the sweet spot it's currently in, or burn badly. Different power, same atty, changes the vapor amount but also every other characteristic simultaneously.
If this question refers to changing to a VV battery, you might not really get that voltage increase. Spinner type batteries, for example, don't indicate if their voltage is reduced by being unable to fully drive the load.