As explained on the manual, the pushback truck is chosen according to your airplane current total weight, the larger trucks requires a weight of at least 170.000 lbs so, check this first.
If you are seeing the small one only on *some* gates, it means they are two small for the large one to maneuver.
Of course, since GSX doesn't know anything about the visual scenery, "too small" means the AFCAD radius, and this can be overridden too, by using the Parking Customization feature. The larger trucks requires a parking with a radius larger than 18 meters, which means 36 meters as the wingspan minimum size.