Basic question is regarding proper placement of insulation and vapor barrier.

The contractor nailed a vinyl backed batted insulation to the concrete walls. Should I leave that up and put PT studded wall up with unback insulation between studs and then cover with a vapor barrier or take the current vinyl insulation down and glue a solid foam insulation to concrete wall before studding and insulating out the wall?

I think the second option is the preferred method, but you may be able to leave what you have there now. How thick is it? Don't want to lose a lot of room. May not want to use a vapor barrier, that would just trap any moisture in the wall. I'm sure you will get lots of advice on this here.

Finishing A Foundation Wall | Basements and Attics | Reader's Digest

You should remove the existing insulation, stud out your walls. You should use treated lumber for the floor plate only. Using treated material to stud out the walls completely is an unnecessary expense and raises some concern about off gassing of that much treated material on the interior. You may be able to reuse the insulation if it is made or can be cut to fit between the studs. You want the moisture barrier on the warm side just behind the drywall. As amricca said you don't want to trap moisture between two moisture barriers or in insulation between the drywall and the moisture barrier.