Why is a 2 percent difference so important?
Its not a 2% difference but I get what you mean.
Voltage drop can effect the proper functioning of some electronics, <3% is the defacto standard (and the actual standard in the marine world), but I don't think there is anything magic about that number, many people shoot for 2% or 1%, and for less critical or more foregiving loads 5% or 10% are sometimes permissible.
There are smarter/more informed people than me who can address how important voltage drop is a for a charge controller, so I'll leave that to them.
But there is another reason you want to use adequately sized wire, power loss. If I understand your situation correctly you have a 45A charge current and a 160ft round trip distance from the PV array to the controller and back.
The formula for calculating power loss is
P(loss)=I^2R, or in plain english power loss = current squared x resistance of the wire
At 8 AWG: P(loss) = 45^2 x .00062 x 160 = 200W loss
At 6 AWG: P(loss) = 45^2 x .00040 x 160 = 130W loss
At 4 AWG: P(loss) = 45^2 x .00062 x 160 = 77W loss
If I've done the math right (and I'm still learning so don't trust me), with 8 AWG you are losing about 1 kilowatt-hour of energy every 5 hours
The other thing is you are potentially pushing the ampacity rating of your wire (depending on the insulation temperature, and the conditions).