MathSciNet has Journal Citation Search feature that might be useful. It lets you select a citing year (from 2000 to 2015 currently) and returns the histogram of total citations listed in MathSciNet from that year to past years (back to 1900), among other things.
With 2015 as the citing year it shows for Journal für die Reine und Angewandte Mathematik 13 citations to 1901-1904, 29 to 1905-1909, and 26 to 1910-1914. For Mathematische Annalen it shows 34, 45, and 111, respectively. For the citing year 2010 it is even more definitive: for Journal für die Reine und Angewandte Mathematik there is nothing to 1901-1908, 7 to 1909, and 1 to 1910-1914; for Mathematische Annalen there are 18 to 1901-1904, 52 to 1905-1909, and 71 to 1910-1914.
So Mathematische Annalen does appear increasingly more "modern" in those years, at least by these measures. You can try different citation years, and with extra work probably narrow it down to 1908 specifically, although I suspect that would require tracking individual citations.
P.S. Search links require MathSciNet access, and may be slow even with that.