It's really amazing how prescient and accurate the late David Akers was when he evaluated U.S. gold coins decades ago. He really knew his stuff and much of what he wrote remains true today. On the occasional times that he was wrong or "off", it is because of newer information that we have today, particularly with regards to hoards and mini-hoards of coins that have shown up in subsequent years.
In the case of the 1861-S $10, Akers' comparison of this date to the 1858-S, 1859-S, and 1860s was spot-on -- all three remain rarer than the 1861-S in terms of overall population. Today's populations of the 1855-S and the 1961-S remain nearly identical and, yes, the 1861-S is still slightly more rare than the 1857-S. The only difference we see today is in the population distribution, where there has been a slight shift to the AU column. EF45 is the most frequently-seen grade for this date, but there are at least two dozen AU examples which, for whatever reason, were not present in Akers' time. Also, there is one Mint State specimen known today -- an NGC MS61 that holds the record price for this date (more than twice the price of the most valuable AU58).