25 degree rise stem vs 6 degree rise stem with taller head tube - how is handling affected?
The weight distribution is affected only by the location of saddle and handlebars related to the wheels. It does not matter whether it is by higher rise stem or higher head tube.

The difference that might affect handling is that system of frame with high head tube and short stem is stiffer than one of lower head tube and longer angled stem. You can feel the difference when pedaling hard, but any modern stem will be far stiffer than old-fashioned quill stems used to be.

There is a financial difference, is your fitter recommending custom frames?