I had a power converter and used the outlet charger and USB that came with the phone. Yes the phone did loose power while on the charger, but didn't go dead.
Anything that's 1A 5 watts is the maximum the phone will accept. I wouldn't advise going over 1 amp.
I used the Griffin charger before. I don't think it kicks out the power as advertised. My phones always charged very slowly with that charger.
Devices I have:
Nexus 7 - Sprint Note 2 - Galaxy S 2 - HTC One - LG G2