This seems to be a fairly common issue.
Upon attempting to charge my Motorola DROID BIONIC with two non-Motorola microUSB wall chargers, I couldn't get the phone past 40%. With the Moto charger, it charges fully (though apparently pretty slowly).
I know the BIONIC's battery is a 3.8v, and my chargers are all 3.7, but the voltage difference doesn't seem large enough to cause a problem. Is is possible the BIONIC can read the difference in the voltage, even if it is small, and is coded not to fully charge on these non-Moto chargers?
Both HTC chargers I've tried were 200mA. It seems maybe the amperage is too low to charge the phone. I'll try and find a higher power one to test.