They both have different risks and hazards, therefore it doesn't really make much sense to directly compare overall hazardousness, especially with such disparity in equipment available to our intrepid adventurers.
For example if you compare risk of dying by hypothermia, it's far more likely cause of death in Mount Everest than on the Moon.
If you compare risk of dying by suffocation (oxygen deprivation), hard vacuum is hard to beat, but you don't have a pressurized habitat in Mt. Everest - which you absolutely NEED to survive in Moon. Moon scores higher here.
Mt.Everest is protected from solar flares by Earth's magnetic field. Moon is not - although acute radiation sickness would require quite a flare.
Might be more fruitful to look at it from a more equalized perspective. If a space ship was stranded on a. Mt.Everest or b. Moon, how long would the occupants survive? Let's assume human occupants (don't want aliens to whom oxygen is poison, that'd skew the comparison unnecessarily).
In both cases ship itself remains intact in the landing but help is not going to arrive before life support goes offline.
Clock is ticking.
Which ship's life support can last longer in different environment?
Which environment provides more hospitable environment for the crew once life support ceases to function?
On Moon, the critical element is ventilation: partial pressure of CO2 needs to remain at low enough level to not become toxic, while retaining the partial pressure of O2 at high enough level to preserve blood oxygen saturation at high enough level for brain activity.
On Earth, critical element is power. The ship will lose heat much more rapidly, so the heaters will need to run at higher capacity than on Moon. It would also be beneficial to keep the ship pressurized as long as possible, but let's assume that ship has similar life support package as airliners in addition to hard vacuum seals - it can take low pressure air in from outside and use it to pressurize the inside. But, of course, this requires power.
It's hard to say which ship would lose power first, or if the ship on Moon would lose their oxygen supply and CO2 scrubbing capacity before the ship on Earth runs out of power, but regardless, the astronauts do have better chances of survival without functioning life support gear on Earth than on Moon.
So yeah, I'll say Moon is the more hazardous place as such.
There is as yet insufficient statistical data on how dangerous place a Moon is - no one has lost their life while in Moon, while a somewhat significant percentage of Mount Everest visitors has perished.
