The StuG IIIB was an experiment and it was very successful. A very good and interesting unit, deducter even says overpowered.
For MP no, this unit is in probably underpowered. I tried to use it, but it is not that great on the one map where you can use it, Iron Cross, Red Star.
For SP however, it quickly gains many stars, is super cheap to overstrength, and becomes a wrecking ball on both enemy tanks and infantry, with its 110% rate of fire. At 3 stars, it has a base of 13 Def, good enough to resist even the T34/41 fairly well. It can be used to drive up to a tank, bombard it, then your panzers can kill or force the enemy tank to retreat. You then move up another panzer to where the enemy tank was, and now your StuG IIIB is not only protected, but it provides cover fire. This is why this unit is ridiculously good for SP.
The problem I think is that for the best SP experience, you have to balance its equipment table differently from MP. Hence when I've undertaken the project to balance unit stats for the DLC content to better reflect historical values and to give a more interesting gameplay experience. I've for instance increased the StuG IIIB's cost by 50%, lowered its armor by 1, and reduced its ROF to 100%.