From a user point of view, their user interfaces both take most people a bit of time to come to terms with. With blender, it took me a few days using it to become comfortable with the way the user interface worked and it took a long time to figure out what the hot keys were as at the time they weren't documented very well. This was several years ago. With current versions of blender and the current documentation available, it wouldn't tke me as much time.
I've never gotten used to Quark. I can get by with it for my needs, but I never have really gotten comfortable with its user interface and terminology. To be honest, I don't have nearly as much time into Quark as I don't have as much use for it.
Most importantly, you need to understand the different reasons these two tools exist. Blender is a 3D modeling program and you are normally editing models based on vertices and polygons. Blender has skeletal and other animation systems which you can use to export animations to CS. There are some nice UV mapping/unwrapping tools available in blender to UV map complex geometry. Blender runs well natively under many operating systems such as Linux, Mac OSX, most unixes and windows.
Quark is a "map" editing program, it isn't really meant to create things made of vertices and polygons. These "maps" are composed of what are normally called brushes and, if the game engine using them supports it, can provide some significant optimizations for collision detection, visibility tests, etc. As far as I've seen, CS doesn't support these features of maps directly, but I'm a CS newbie, so I could be wrong. There is support for texture mapping in Quark, but its limited to working well with the "brush" system. Quark has no, or very limited, support for animations. Quark only runs natively under windows, although I understand this will eventually change.
If you were making maps/levels for Quake or Half-Life, I'd say use Quark as it was designed to make those maps with all their special limitations/features that those game engines support to make them efficient for those engines to use. Blender doesn't do this very well as its not its intented purpose. However, if you're making something based on vertices and polygons, blender works much better at that as that was what it was built to do. My current understanding of CS leads me to believe that it works natively with objects contructed of vertices and polygons. Thus the way blender works with the data is closer to the way CS works with it and anything made in Quark needs to be converted to this representation since "maps" and "brushes" aren't represented this way.