The differences in profile and size are represented by the Size characteristic, and the assault guns tend to have a bit lower values than tanks based on same chassis. For example, Stug III is size 3 while Panzer III is size 4. Similarly, T-34 is is size 4 while SU-85/100/122 assault guns are size 3. Smaller size makes unit harder to spot and hit with shooting.
One significant in-game restriction with assault guns is that immobilisation damage tends to make them something of sitting ducks in a lot of situation, if the enemy can avoid entering their field of fire and move to their flank for the final shot.
The other in game difference is spotting from turreted vehicles is slightly better than non-turretted ones.
I was away from my desktop at the time so I could not recall if there was a size difference or not, so thank you for confirming that. I also didn't know that about spotting but it makes sense. Learn something new about this game every day.