Kneading dough - significance of warm hands
The temperature influences the speed of rising, but to significantly change the dough hardness, you need a very cold temperature. Even if your hands are "cold", they are certainly above air temperature, and firming up dough through coldness is only possible if you use very cold ingredients, below fridge temperature (4 Celsius).  

It could be kneading technique, if by "technique" you mean the amount or type of lubricant added. Some people knead in a bowl of flour until the dough stops sticking. This will give you a very hard dough. Some use minimal amounts of flour during kneading, and yet others may knead without a lubricant, or using oil or water. Again, this is a very likely culprit in achieving different grades of softness. 

A somewhat more "hidden" influence would be the direction of kneading (do you align your gluten into sheets or ropes, or do you just knead directionless) and the relaxation time given to the dough during kneading. The length will also play a role, longer kneaded dough develops more gluten and becomes tougher. But while these differences will contribute to a harder (actually "tighter") dough during kneading, they should be reduced after proofing. And the baked bread won't be harder, but slightly more translucent and chewy. This is because they result in more gluten, and what you describe (bread harder after baking) points to more flour. 

So, if there is no difference in lubricant addition, one of you is probably measuring differently from the other and ending with a different ratio. Maybe one or both of you measures by volume, or is using a badly calibrated scale.