I can tell you that the parking brake does not hold all of the wheels like applying the foot pedal does. I have encountered an issue twice due to this "issue". The first was on a snowy slope at the entrance to a campground in Flagstaff, AZ. All was well and we stopped just fine. I set the brake, took by foot off the pedal and began to slide right down that slope. Foot back on the pedal and we stayed right there.
The second time was apparently due to my brakes not having been adjusted in awhile (manual adjustments required on my coach) and we were at the World of Fun campground in Kansas City, MO. The check in area is on a fairly steep slope and even on nice dry asphalt, the coach started rolling down the hill with the parking brake set. Not good!
Additionally, remember that when the brake is set only the rear wheels have any braking applied. If you have and use jacks of some kind you MUST keep the rear tires firmly planted to Terra Firma or the coach could roll off of those jacks causing damage to the jacks and any surrounding objects.

How Parking Brakes work-

In essence, these are identically the same brakes that are required by law on semi-truck combinations.  Extremelly strong springs lock the wheels on axles that are affected when air pressure decreases below about 80 psi.  This absolutely locks those wheels.  The air compressor must build sufficient pressure before the vehicle can be moved, or in emergency recovery of a vehicle with broken air lines, the parking brake chambers must be "caged" (something only trained mechanics should do).

Parking Brakes are not installed on "steer axle wheels.  On tractor-trailer combinations, the drive axles on the tractor and all axles on the trailer are locked.  This is 16 of the 18 wheels.  On motorhomes, only the rear wheels are locked.  This would be 4 of the six wheels. (a tag axle may add to that)  Commercial tractor/trailer combination vehicles do not have leveling jacks and are positively immobilized.

In essence, the purpose is to stop the vehicle automatically should air pressure be lost if an air-line is damaged.  Yes, they are labeled "parking brakes", but are much more. 

Bottom Line-  It is not a matter of "parking brakes" holding a motorhome on an incline, the culprit is the use of rear leveling jacks that take the weight off the rear wheels that secure the motorhome in position.

Extreme caution must be used when using leveling jacks on unlevel parking surfaces.

Roz gave a very good description of how air brakes are supposed to work.  HOWEVER, I highly recommend the use of chocks anyway.  I have personally seen an instance where a parked 18-wheeler rolled down the slope of a parking lot and "bumped" a car parked at the restaurant.

While I never got a good explanation of how 16 brakes failed, I can only think that enough air from a reserve tank was leaking past the cutoff valve to release the brakes.  The truck had been parked for the night and shut off and the driver, me, was in the restaurant eating supper.

One of the people sitting in the car that was "bumped" came in asking about that "black and white" truck.  They watched the truck slowly move down the parking lot and assumed someone in it would apply the brakes.

So, it has since been my belief that when parking anything with air brakes, a set of chocks go down at the rear wheels.

THAT incident has to be my most embarrasing moment while driving trucks professionally.

Terry