Im guessing when you say USB your referring to the Micro USB connector on the end that plugs into the phone. The end that plugs into a computer or wall charger is the USB side.
Not trying to be a **** but just trying to get us all on the same technical page. LOL
Anyway, Micro USB chargers are supposed to comply with industry standard 5 V DC out put. The amount of current can vary from 500mAh to over 2amps. The phone can accept any of the current out put as it will limit the amount of current its draws. Usually this is built into the Kernel layer of the phone. So your note 3 charger should put out 5V DC @ 2amps. (max) as it can also output less.
The HTC One will draw on average 750mAh to 1.5Amps or 1500mAh. The higher the current the faster it will charge.
So any micro USB charger should work with these units. I prefer to stick with name brand like HTC, Samsung, LG, Motorola, Blackberry when charging my phone. NO need to use a cheap nock off that could potentially fail and fry my $650 phone.