I am a native speaker and I feel that I use both of these constructs. Have I been mistaken all these years? If not, what's the subtle difference between the 2. Looking for other opinions. My thoughts are.
"Would you prefer to walk or run" = Would you prefer to walk? OR Would you prefer to run? Asking this as they are about to depart to somewhere.
"Would you prefer to walk rather than run?" Someone saying they really don't want to run...so giving another suggestion before departing.