It's now 2023 and the performance step change of str2num is still there but now in a different place...
str2num is still 4x faster then str2double in this situation.
(R2022b, Win10)
str1 = num2str(rand(15384,1)); %list of numbers as char, 15384-by-10
str2 = num2str(rand(15385,1)); %list of numbers as char, 15385-by-10
timeit(@()str2num(str1)) %0.002 sec FAST
timeit(@()str2num(str2)) %0.046 sec 20x slower
timeit(@()str2double(str1)) %0.009 sec 4x slower
timeit(@()str2double(str2)) %0.009 sec 4x slower