Rate of deaths from stairs = 56 fatalities per 100 million miles.
Rate of deaths driving a car = 0.56 fatalities per 100 million miles.
Stair data: 3,800 fatalities per year over 1,953 billion stair uses* which covers 6.832 billion miles allowing a stair to be 119″ high (~10′) with a 7″-11″ stair ratio (32deg pitch) giving a travel distance along the stair of 222″ thus 286 stair flights per mile. *Centre for Building Technology, National Bureau of Standards 1979, Guidelines for Stair Safety (1975 data). The comparison assumes that stair safety has not improved 1975-2011. If there is newer data it would be useful.
Driving data: 16,430 driver (not passenger, motorcyclist,etc) fatalities over 2,946 billion mile for USA 2011. The denominator here is the total travel hence will not be accurate as it will include motorcycles (which are not on the top line) but motor vehicle only distance seems hard to locate. The total road fatality rate is 1.1