I used to wear boots a lot but am a convert. These days, I'm only throwing on the boots when there is snow or significant broken rock/talus which an beat up your soles. The runners are just more comfortable.
If you're backpacking, the boots will keep your feet more comfortable and resist fatigue due to the support, but wear your runners more during the daily training and exercise to build up those little muscles and toughen them up. No comparison if you're scrambling. I've worn a pair of 5-10 approach shoes for the North Ridge of Lone Pine Peak and never threw on my climbing shoes. Only issue was getting my feet wet at night on the way back while crossing a creek going cross-country.
My feet are particular about the boots I put on and have a tendency to get blisters. No issues with any runners/approach shoes.
