Forza has always been catered to a larger crowd, IMO, whereas GT is catered toward the "enthusiast".
Over time they have grown toward each other, in such a way that they are near indistinguishable, as far as their demographic target goes. I guess you could also say that, really, Forza has just gotten more realistic with time, and that GT has basically always been the same.
Tecnologically, with regards to platform, the PS3 should be able to simulate vehicular physics more realistically (more CPU horsepower), whereas Forza should look better, because racing games don't require much beyond the simulation and terrain, in main memory, and the X360's flexible memory architecture, and flexible GPU pipeline should really shine in the genre, which is naturally lopsided, as far as system resources go.
In a sense, Forza has always been a natural fit to the 360, for that reason, and perhaps GT is a natural fit for Sony's console as well.