I really think that to quantify something like this you'd need to hold other variables constant so the differences in mileage, pace, etc. prevent any sort of conclusion. The one guy I was thinking of who kept his volume the same but went from singles to doubles was a guy called Bob Scharf who no one here has likely heard of but was perhaps the best distance running in the DC-Baltimore area in the middle and late Sixties. He'd been doing 120 mpw in one run. He told me that he ran in the 1965 AAU six mile championship in San Diego, the one where Billy Mills and Gerry Lindgren tied for the world record and Lindgren told him to keep to the same mileage but do it in two runs a day. Scharf told me that it made him a much better runner but I don't have any specific times for him other than a 2:22 marathon, which in those years made him one of the fastest in the US.
Barry Magee told me that when he started with Lydiard he was doing 100 mpw in his base phase in just one run and it made him a "national class" runner. Then he added a second run of 3-4 miles and said he became "world class." But again, I have no before and after times and the switch to doubles gave him more overall volume. Jack Foster had a similar story. He'd always been a once a day guy but before his 2:11 at age 41 had a few weeks of doubles where he was doing around 100 a week. So he too, made a big improvement, 2:12:17 to 2:11 something but he too was running more with the doubles than with the singles.
I went from one run to two in 1973 and began getting much faster like 38:00 for six miles to 15:34 for 5 km, 32:20 for 10 km, and 3:15 in the marathon to 2:41 eventually. The mileage got much bigger, 50 or so to 100-150. Then I seemed to stop improving and went back to one run a day, volume to 75-90, and got to 2:35 for the marathon and 15:33 for 5 km. But that came after years of doubles and bigger miles. When I was running once a day before 1973 and doing 80 or so a week I was nowhere near as fast as in that second round of 80 or so.
What I found was that I could run up to 110 or so in a week in one run and feel okay but getting to 115 and beyond in one run was a real drag. Getting out for runs of upwards of 15 miles every day was very tiring and I think the overall pace got slower and slower. Doubles were much more useful. People keep revisiting this topic but to me, the almost universal practice of running twice a day at least on some days by national and world class runners should have settled this question long ago.