In order to get the area of intersection, both input geometries have to be polygon type geometry, and you need to choose the result dimenstion to be esriGeometry2Dimension. And you will need IArea interface to get the area.
ITopologicalOperator t = polygon1
IGeometry g = t.Intersect(polygon2, esriGeometry2Dimension)
IArea a = g
a.Area is what you want.
There is no behavior change between 9.3 and 10 for Intersect method.