Though Alex's answer has its point; but as the OP confirmed the second adapter in question is a HTC charger, I hold it more likely that a special "PIN usage" is the cause. As I explained in my comments to the question:
PinOuts describes how the PINs of the USB connector are used in general.
screenshot from PinOuts.ru
Note the "x" PIN which, according to the description, may be connected to GND.
Now to my observation: As I was annoyed by the very same problem, I decided to dig a little deeper. I tried 3 different cables with the HTC power unit versus two other power units (one Motorola, one generic) on my Motorola Milestone 2. In short, all cables behaved exactly the same: connected to the HTC power supply, they caused the very same behaviour described in the question, i.e. unpredictable reactions to the touchscreen. Connected to any of the other power sources, there was no such effect. So the cause very clearly was the HTC power supply.
If EMI were involved, as Alex suggests, the same strange behaviour should appear here daily, as that HTC power supply is connected to a power source (and such must emmit those electro-magnetic disturbance), and my devices are often positioned not much more than 20cm from it. A connected cable might bundle that, true -- but I still hold my theory for more likely. And as one can find by looking at this XDA thread, HTC chargers do obviously use a different PIN layout -- which adds its weight to my arguments.
Besides: Other devices connected to the HTC charger (I tried with two tablets, none of them a HTC) did not show the effect. So with the EMI argument, the resumé would not be "HTC builds lousy adapters", but "Motorola builds lousy displays" ;)