I'm not sure I agree with lower speed, at least dependent on which group you mean.
The armies in europe were large groups, with heavy weapons and armor, slaves and campfollowers and construction materials/tools among other things. They often "foraged" or otherwise looted the surrounding lands, slowing them down.
The armies in America will have worn far lighter weapons and armor, due to the low availiability of iron.
According to a quick googling, the Aztec army is estimated to have moved 18-32 km a day, in part helped by the extensive roads in Mexico.
A medieval army could be expected to reach those speeds, only when supplied by boats (at an estimated 20 miles per day = 32 km).
When foraging they were restriced to 5-10 miles a day. (8-16 km).
As such I see no reason to change the speed, beyond what is required by the new scale of the world.
Source:
http://www.au.af.mil/au/awc/awcgate/army/medieval_logistics.htm
For the Aztecs, I used wikipedia

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