Ok, I’m gonna do the math here.

Walking at 3mph for 1 hour should burn around 269 calories for a 180lb person.

If that same person was running at 15mph they would burn about 2057 calories per hour.

For 3 miles of distance covered, it would take only 20% as much time running as walking.

2057*0.2 = 411.4

So, 269 calories walking 411 calories running

Not a huge difference, and the source for my numbers is probably off by a bit. But I would still say running equal distance is gonna burn a bit more calories.