Re physics: Yes, but there are statistics for calories burned from such activity.Since there are several loads, you could just find out by experiment. Take the first load one way and the second load the other way and compare how exhausted you are after each of them. This isn't going to be a very accurate measurement, but it's way more accurate than a theoretic calculation would be.
Describing the effort of carrying something is quite difficult, because from the physics point of view, you're hardly doing any work at all, but due to the way muscles work, they will get exhausted nevertheless.
In the end the experiment is the deciding thing in science. It doesn't help, if one way should be easier on you, when you feel the other way afterwards.
Tiredness can be hard to compare when the activities have an unbalanced intensity, such as here where by the time you get off the subway, you may have already forgotten any tiredness felt from caring the load to the subway.