Phone charging problem with vehicle power adapter
The pictured charger is likely a super old type with a linear regulator limited to 500 mA (lm7805) or a first generation switching regulator and limited to 750 mA (Mc34063). I'm  assuming this based off the case it has, which is typical for those types of chargers. Newer chargers have higher capacity regulators/circuits, and are capable of delivering multiple amps.

They probably don't have the signaling resistors for any recent phones to know what current they can draw, as older cell phones did not require them and only charged at slow currents. So newer phones self limit to standard usb current of 500mA or less, as if they were connected to a regular computer usb port. Look at the usb battery charging specification or the data available on iPhone charging signalling. 

And they are also likely set to 5.0 V, instead of a better 5.2 or 5.3 volts, which allow for voltage droop as current draw increases. A 5V supply with a cheap usb cable with small cable gauge/size, i.e. higher resistance will see a higher voltage drop at higher currents, bringing the voltage at the device down to outside of USB specs. For example, my Galaxy S7 will charge at a higher rate from a 5.3V 1A supply compared to a 5V 1A supply,  with the same wire. The phone detects the voltage in determining how much it can draw.

All this makes your phone discharge faster than it can charge, unlike a properly designed or up to date charger. Newer standards like Quick Charge are even more complicated, requiring variable voltages, higher current, and complicated signaling or negotiation.