I think Finsbury Park will be favoured by many because, especially once lifts are installed, FPK could be a place to get trains from STP, KGX and MOG. The best of three worlds!
Based on how things are at the moment, I think people will certainly use it for the trains which will run Potters Bar-Hatfield-Welwyn GC and beyond. I'm less convinced people will use it so much for journeys to further out - simply because this gives them last pick of the seats. People will tolerate this for a 20-minutes journey to Hatfield or Welwyn, but not if travelling further. At places like Hitchin it's common to see people arriving on the platform 20 minutes before their train in order to be first on.
However the platforms and the subway are perhaps not geared towards having people using the station more like a terminal station
Perhaps being the understatement of the century!
The station simply can't handle large volumes of people, and this includes the LU part too. Again, if the Thameslink Programme expects Finsbury Park to function as a major interchange, some pretty major rebuilding should have been carried out - although looking at the place it's hard to know where to start short of completely flattening the place and starting again. Virtually everything about the station is inadequate for large numbers of people - the stairways are too narrow, there are 90 degree corners and pinchpoints everywhere, the subway is too narrow, the interchange to the Underground is inadequate (how many stations in London use spiral staircases other than as an emergency exit?), and there aren't enough Underground platforms to cope with large volumes of people arriving from elsewhere.
I saw what happened on the well-known 27th December fiasco a few years ago, when I passed through on 2x313s, the station was in complete meltdown to the point where it was clearly dangerous. People could be seen trying to get to the train, but were impeded by other flows of people. Had commuters been involved, under time pressure to get somewhere, I think there could easily have been injuries or worse.