It's all good
I do a mix of both...I love running and do about 5mi x3 days a week. I also hike all I can.
I think the key is heart rate... I can amble along at 2.5mph on flat ground and never get a heart rate increase, I burn calories but don't get much workout from it- some people can and do. That same 2.5mph with 3k' vertical is a whole different story.
For fitness, the heart rate monitor is your best friend.