Not necessarily true.
Even when charging wired, different methods (USB vs AC adapter) charge at different speeds (rates), dependent on the amperage, despite that the voltage is the same. I'm not sure what kind of max amperage the Nexus 5 can handle, but by way of comparison, your USB port and smaller duty AC adapters push out 0.5 Amps, while the heavy duty ones push 2.0 Amps; the latter charges significantly faster.
The same can be applied to wireless charging, with the caveat that some of the charging throughput is lost through
significant inefficiencies with wireless charging.
On the original wireless smartphone charger, the Palm Pre and Palm Touchstone, the Touchstone was notoriously fickle, and would not generate a strong enough EM field for the phone to register charging if you hooked up an AC adapter with anything less than 2.0 Amps of current.
And even then, it charged notably slower than hooking up a 2.0A charger directly to the Palm Pre. It charged roughly as fast as a 0.5A charger hooked directly to the Pre.
So yes, there is a measurable difference between wired and wireless. That said, neither should affect battery life to the extent that you charge both to 100% capacity; the difference only lies with how fast the battery charges, not any qualitative differences after the battery is charged.