Power = work/time
Force=mass*acceleration (= weight here basically)
One of the most difficult things to accept for some people , is that with no D, there is no work. I.e. you can struggle and sweat to hold up 100 lbs until you collapse. But if you dont move it, you havent done any work on it. The faster you move it thru the same distance, the higher you power output is, but the same work is being done.
If you have 100 lb wt on wheels, and roll it horizontally, did you do any work?
In a frictionless world, Nope. Even though you might move it, the only resistance to it moving horizontal is friction. In reality you know that may be a substantial amount depending on how good the wheels are and what the surface is. Same applies when your body is the "wheels", its called innefficiency.
The real base work you do would be lifting your body weight , the vertical distance you lifted it by going uphill. That doesnt change, its the same in both cases.
You need a higher power output to do so in a shorter time, thats why you are more tired.