Which burns more calories stairs climbing or walking?

When it comes to burning calories, your heart rate is much more important than what it is that you are doing. If you can reach and sustain the same heart rate for the same amount of time you will burn pretty much the same amount of calories regardless of activity.

Most people would reach a higher heart rate when walking stairs, so they'd burn more cals/minute that way. Whether they'd burn more cals in total that way depends on how long they're able to keep it up.

Let's say stair walking boost their heart rate from 80 to 150, and that they're able to keep it up for 10 minutes. That's 70x10 = 700 extra beats, and extra calorie usage.

Let's say brisk walking boost their heart rate from 80 to 130, and that they're able to keep it up for 30 minutes. That's 50x30=1500 extra beats, and extra calorie usage.

In this case brisk walking would burn the most calories.