I can confirm that for my MacBook Pro, charge current is increased above 500mA when using a POWER ONLY cable.
My understanding is that if the phone is connected via a POWER & DATA cable, the 'consumer' negotiates with the host for how much current is passed over the cable. When the negotiation asking for higher current is not successful, the available current is reduced to the standard (USB 2.0 defined) 500mA amount at 5V.
In the case of the POWER ONLY cable, no negotiation can take place and thus, the maximum usable current is provided by the host to the client or 'power consumer'.
When running on battery power (±80% state of charge), my early 2015 13" MacBook Pro (2x USB 3.0 ports) was able to charge my OnePlus One (±60% state of charge) at a maximum current of about 1750mA.
No change in charging current was observed when the laptop was connected to the mains or powered by the internal battery.
No change in charging current was observed when switching from one USB port to the other.
During the phone's charging process, keeping the screen ON resulted in an average charge current of about 700mA. When the screen was kept OFF, the average charge current increased to about 1750mA as previously mentioned.
As the phone battery reached a higher state of charge, the charge current was gradually reduced. At 67% state of charge, the maximum current was 1650mA. Note that this is consistent with the general behavior of lithium ion batteries. The battery controller will reduce the charge current in order to reduce the stress the battery's chemistry experiences during repeated cycling.
According to another answer, using a thunderbolt-powered USB hub in combination with a POWER & DATA cable seems to achieve higher charging currents as well. This, however, requires an additional dongle which is a solution I did not prefer.
The following is taken from an answer to Why is charging from computer using USB slower than using an outlet?
The reason your android device draws less power from your USB connection than from a wall adapter is because of the USB specification. This can be side-stepped by shorting the data wires in in the USB cable, which will switch the phone or tablet into wall mode where it can draw the full available current. The amount of current available will vary considerably from PC to PC.
The reason the specification exists in the first place is that the voltage to the computer's USB ports is usually supplied via the motherboard by a single loop connection which services all of the USB ports at once. Being only a few microns thick, this circuit is not able to deliver the same current as a dedicated charging wire. It is highly improbable that you will 'burn out your motherboard' by trying to draw the full available current through this circuit (although it is theoretically possible if your computer was a total P.O.S. to begin with). What is more likely to happen is that you will exceed the manufacturer's design specification, thereby denying sufficient power to any other USB devices you have connected, and/or other internal circuits which can cause the PC to crash. This is the very same reason it is recommended you use powered USB hubs.