Is there an important difference between these two power adapters

they are both adapters made to be able to accept a usb cord and convert it to be able to be plugged into an electric socket (like many mobile phone adapters). they both have the same input (100-240V, 50/60Hz, 0.2A max), but their output is different (5.0V --- 1.0A and 5.0V --- 0.5A). The question is not is there a difference--of course there is--but does the difference matter?

Yes, there is the obvious difference. If you are charging a battery, all other things being equal,, the first will charge it in half the time. But it could be that the charger electronics limits the current to 0.5 amp or less, in which there is no difference.

If you are just using it to power a phone, and if the phone takes less than 0.5 amp, either will work as well. But I doubt you are using it that way, as they all have a battery that could need charging also. But again, it depends on the charger electronics.

Bottom line ,get the more powerful one if the prices are comparable. It may be better, it may not.

If what you are going to use it to power requires less than 1/2 Amp, (0.5 A), then there is no difference., If the device requires between 0.5 and 1.0 Amp then the heavier-duty unit is needed.,