From what I gathered, they see Fox as Lovie 2.0.
However, Fox has a much more impressive resume at this point. 2 superbowls to 1, more playoff appearances, more championship game appearances, and the key factor, unlike Lovie, John hires experienced NFL head coaches and then trusts them to do their jobs, vs Lovie who would hire shit coaches and then we'd be on our way to an 8-8 season again.
Also, for as much as people talk about Fox's record, that last 2-14 year really skewed the percentage, and that was when their talent was all shit or hurt, and shit talent can be blamed on the GM.
Fox is far from perfect, but he is solid, and a proven commodity for rebuilding a franchise, which he has done, twice. Right now the Bears are in no place to try for someone who is a high risk - they need to rebuild this thing, and Fox CAN get the job done.