All three of my drain pipes are (only) 1". I think the original Herbie method with the primary drain and a trickle e-drain used the same size pipes I believe. If I were to do it again, I would try to use larger pipes just because. Aside from the 3 standpipes, I have a 1.5" return T'ed to two 3/4 braided lines with loc-lines. I also have a pipe to run wires down to the overflow so wires are hidden. All piping hidden in my internal overflow (I have a peninsula style, so hiding everything was important to me).
In retrospect the wire pipe was a cool idea, but having room for larger pipes makes more sense I suppose. Having said this, I don't think the 1" pipes are lacking in terms of turnover. The second pipe has a slight trickle and the third is completely dry. I do use a sock for the second drain.
For reference, I have a Waveline DC 10000 II rated 2800gph max, I have about 5-6 feet head pressure, with a few 90* and 45* PVC angles. I run the pump at 7 of 11 flow settings. To be honest, I could crank it up max and I still think my 1" pipes could handle as I'd open up the drain a bit more.