It really depends on your health goals and the way you want to conduct a fitness program. If your goal is general health, it would be better to alternate between the two, as this would develop both long-term aerobic (with oxygen) strength as well as anaerobic (without oxygen) strength.
It's important to consider something called the 'Principle of Specificity". Basically, it means that you should train what you want to develop. Swimmers, swim; runners, run.
If your goal was to run more explosively, then it would be better to run the one mile. If you wanted to work on your general fitness, (with no particular athletic goal), then perhaps it would be better to walk a longer distance.
People will probably mention the number of calories burned doing each activity, and use that to compare which one is better, but it never hurts to do both in equal measure. It also depends on your situation, mood, and level of fitness.