Drywall over furring or over stud?

I've got a room I'm redoing and had to remove some wood paneling. This was nailed on furring strips over studs. I can mount the drywall over the furring strips or remove them and screw over the studs instead.

My preference is to mount on studs directly because I feel is firmer and would give me a way to mount other stuff on the walls in the future (clock, paintings, and/or tv). The only problem with this is that the furring is already on there. In addition, the slab ends around some perimeter wood form that would be exposed even more if I mount directly on the stud. This would generally not be a problem except I don't want to install baseboards. Also; would have to remount electrical boxes

Any suggestions/ideas?