Saw a series on NetFlix not long ago which included a description of battle from a StuG commander & they used them almost like tanks. They were, apparently, quite manoeuvrable & able to bring their guns to bear as fast as the T-34's they were opposing. Their problems came if forced to withdraw from the battle, as to keep their guns on the enemy they had to reverse all the way.
Of course, you have to remember that, unlike S-tanks, they had limited traverse & the full range of elevation on the gun.