Breathing oxygen allows the body to function at a higher altitude than breathing normal air since it maintains the partial presure of oxygen needed by the blood. Flight crew oxygen masks are automatically programmed to supply the right mix of oxygen and air as the cabin altitude increases during climb, and if a depressurisation occurs will shift to 100% oxygen. Of course the mask will not do any good if it is not being worn, and it is assumed the pilots have 5 seconds of useful consciousness above 35,000 feet in which to grab the mask and put it on. But at some altitude above 30,000 feet the partial pressure of oxygen even with 100% flow is equivalent to an altitude above 10,000 feet, and the normal person will begin to suffer from hypoxia. In order to maintain enough oxygen to reach the blood at a level that will allow normal function above that altitude it must be fed to the lungs under pressure, which can be achieved by using a pressurised mask; most airline masks are capable of that (Emergency flow) until, above around 42,000 feet, a pressure vest or suit is needed to hold the chest tight so that oxygen can be fed in under high pressure. If the suit is not worn, the pilot cannot breath out against the pressure. Even at lower altitudes where the suit is not needed, it is weird to use a pressure mask since the pilot relaxes to take in oxygen and has to force it out consciously and with effort. Breathing is a chore. Not doable for passengers. If depressurisation occurs at Concorde altitudes an immediate descent must be made, because the passengers do not have a pressurised mask or pressure suit. At the lower altitudes flown by conventional airplanes it is not so important to start down as quickly, since the flight crew can survive for extended periods using the oxygen masks provided, and most passengers, even if not using oxygen, will not suffer long term effects so long as they are not kept at cruising altitudes for longer than four minutes or so. If they are breathing oxygen from the drop down masks they also could manage for as long as the oxygen lasted, even though their masks are not as sophisticated, but there is always one or two who do not know how to use the mask. Of course if they follow the normal airline safety brief, where the main aim of the flight attendant is to avoid mussing his/her hair, they will never learn how.
I am not sure of the exact altitudes for the situations I have given above, anyone who has accurate information can flame me freely.