Quake uses Axis Aligned Bounding Boxes (AABBs) to represent game objects in the collision engine. Basically, all objects are treated as cubes that do not rotate with the model, but instead stay oriented with the world axis.

At one point Gamestudio used this same system, but now it uses a combination of different systems depending upon what objects are being tested. When using the c_move() instruction to move an entity, ellipsoids are used to handle collisions between entities and world geometry, and OBBs (oriented bound boxes, which rotate with the model) are used when two entities collide with one another.

More info on this page:
http://www.conitec.net/beta/collision.htm

Needless to say the system is finicky and difficult to manage. Understand that unless you know exactly how to use this collision system to your advantage, you will end up with a sticky mess at the end of it. My advice: write your own robust collision system with the aid of the Gamestudio functions, or find someone willing to do it for you. But whatever you do, don't abuse the stock Gamestudio movement functions, or you will end up with something that is very difficult for you to control as a game designer.