There are of course many different wire sizes. AWG 18 wire has a diameter of about 1 mm. I think most of the signal wiring was smaller than that precisely to save weight, but the power wiring would undoubtedly have been much heavier. Apollo's primary power supply was 28V DC, a low voltage that requires fairly heavy conductors to carry a lot of power. Some of it was also distributed as 3-phase 115V 400 Hz AC, but it was mainly for devices that need AC (like induction motors) rather than to lighten the wiring. In those days, AC inverters were one of the heavier and less reliable subsystems on a spacecraft.
Copper is a dense element, almost 9x as dense as water. A liter of the stuff would have a mass of almost 9 kg; one cubic foot (28.3 L) would be 253 kg! Of course, part of each wire is the much less dense insulation, probably Teflon.
Modern electronics allows spacecraft wiring to be vastly reduced in weight, bulk and complexity, also simplifying connectors. That's important because they're still among the most unreliable of all electrical components.
One advantage of modern electronics is lower power consumption, allowing lighter power wiring. Power semiconductors now make DC-DC conversion easy and efficient, so it's easier to use higher voltages for more efficient transmission over greater distances. The ISS, for example, operates its solar arrays at about 160V DC, and utility power is 124.5V DC. (Of course, the ISS is much larger than Apollo.)
But the real breakthrough in wiring has come from digital electronics. Every spacecraft has zillions of sensors and control devices all over the place, and in Apollo each required its own dedicated wiring and connector pins.
The wiring harnesses were massive, hard to make and easy to damage (remember Apollo 1). Redundancy was hard to provide. Analog signals often had to go significant distances, creating noise problems. Quite a bit of wiring passed between the CM and SM, or between the two stages of the LM, requiring large explosively-driven "guillotine" cutters for separation. That in turn required "deadfacing" relays and switches to disconnect each line and prevent a short circuit when it was cut.
Now you make a high speed digital bus with just a few wires, route it all over the spacecraft and attach it through bus interface electronics to each sensor or control. Being digital and usually differential (a balanced twisted pair), the bus is inherently much less susceptible to noise. Analog sensor signals are converted locally to digital before going on the bus. The reduction in wiring complexity is so great that it becomes easy to add another bus for full redundancy.
