One thing to consider about the 13.0 grain load is that it is for a Hornady 124 grain XTP-HP. They are longer and I think harder than the Speer Gold Dot 125 grain bullets. So, pressures may be somewhat different.
Also, has anybody checked on the primers used in the two data sets? Using magnum primers would probably make quite a difference.
Accurate had at one point used standard primers for many of their AA-9 loads, but switched to magnum primers for several cartridges because of concerns about substitutions by handloaders. I know that happened with the .357 S&W Magnum, but I don't know about the 357 Sig loads without looking at the manuals, which are not at my current location.