Walking vs Biking a mile

Every Diet has to obey the first law of thermodynamics: Burn more calories than your uptake.

This guy analyzed the fuel milage of a human. The comparison could be sound:

Activity            MPG food MPG    gas/lard    kWh/100-mi

Biking, incidental      290           1300         2.8

Biking, long-haul       160           720          5.1

Walking, incidental     75            340          10.4 

Walking, long-haul      40            180          20

(I don't have a good idea how to format this table right now) Note that those are approximations, good for a factor of two. But still this tells us that walking burns more.

Since its a "mile" that is in question I am agreeing with JohnP's answer I just wanted to add a few tips

1. Once walking gets easy start Jogging this will make sure that you keep your heart rate elevated.

2. If you have a android or and apple device there is an app from Digifit called Digifit or Ibiker or Irunner they are all the same choose either one of them, the good think about it is that it works in sync with MyPalFitness and it will update your calorie needs, and please note that this app is only usefull if you buy their heart rate monitor you will also need to get the in app purchase for about $8 on apple devices, the reason for that is so that while you walk jog or run you can make sure to keep you heart rate elevated at about %55 to %65 of your max heart rate.

If you are going strictly by distance, then walking will be more beneficial simply because you will spend a lot more time to cover the same distance. Say you are going 4 miles. A moderate biking speed, you will cover that distance in about 20 minutes. To walk it at a moderate speed will take about an hour.

Where it makes a difference in a lot of exercises is the impact that your body takes (almost none with biking, more with walking), and the intensity in which you do it. Higher intensity exercise does burn more calories, but you typically spend less time doing it, so it can be kind of a wash.