I would have classed the JSU 152 as an assault gun more than an SPAT vehicle.
The 152 mm was an artillery piece first and foremost, with a relatively limited AP capability in terms of its size. Sure, it would stop most tanks with a good hit, but it was designed as a bludgeon not a rapier (to use an anolgy).
As Firefly (?) has pointed out, the nearer German equivalent would be something like the STUG or Brumbar, rather than Jagdpanther or Jagdtiger. I’m not sure the STURMTIGER really had anything like it at all! Possible the CHURCHILL AVRE with a petard mortar.
The assault gun concept was a solution to a problem nearly as old as the tank itself - that of the turret ring. In a normal, turreted tank, you need a lathe of gargantuan proportions to make the turret ring, and this can be the limiting factor in your tank production capacity. The bigger the gun you want to mount in the turret, the bigger the turret and thus the bigger the turret ring (apart from the actual physical size of the breech, the turret ring also has to transmit the recoil stresses to the hull).
However, in an assault gun, you don’t have a turret ring so you don’t need quite as many machine tools to make it, and the weight saved on the turret ring, traverse mechanisms etc can be used to allow thicker armour (usually over the frontal arc) on the same chassis as the “parent” tank.
Interestingly, there were a series of experiments at the Royal School of Artillery, Larkhill, into the AP effects of larger calibre artiller pieces. One of the most effective rounds was a 155 mm shell filled with concrete. It just knocks a big hole in the tank.
I also found out a few years ago that a number of the large USSR artillery pieces seen in the May Day parades of the 1950s and 60s were fakes designed to fool the West. That 310 mm SPG was apprently a JS series chassis with a big tube on top that looked like a gun. The USSR truly were the masters of maskirovka.
edited to add paras 4 & 5
