For mids and tweeters it doesn't matter as you are above the baffle step and usually looking to shed some spl. Small wire/ high DCR can work well with tweeters.
I'm using wire repurposed from a motor salvaged from the scrap bin at work for the tweeters. It's probably 20 or so gauge and it does up the resistance vs heavier gauge wire. Just have to be sure and include the resistance in the sim because it does make a difference.
I have had a couple instances where larger gauge and resistor sounded better than smaller gauge and dcr to make resistor value. Honestly, larger than 14 is silly big, and I try to use 16 whenever possible. 18/20 air to me are only good enough for conjugate networks, or cheap projects, and minimum 18 on steel laminates. I only use p-cores in conjugates now due to distortion, litz should only be on woofers as it messes with tweeter and mid FR due to higher Xc, and only use laminates for woofers if you don't mind some extra slam.
It's easy in a simulation to increase the series resistance to see what effect a higher DCR smaller gauge wire inductor has on the response. Depending on the circuit location, it could be significant, or very minimal. The important thing is just to make sure that it's taken into account when you do the design so what you build will match with a high degree of accuracy. For the most part, low DCR for the woofer inductor is preferred which is why you often see cored inductors here. For a tweeter circuit, the difference between 18/20 AWG and 16 will not be easily noticed, especially if you've designed your circuit with the extra 0.25Ohms that using a small AWG inductor will add.
Looking at an inductor for a woofer, 3.3mH value for example. 16AWG air cor is 0.66Ohms, 20AWG air core is 1.43Ohms (0.77Ohm difference), and a 15AWG sledgehammer steel laminate is 0.185Ohms. Now there's some real difference that will make a change.
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