The big question is,did the Arnold shader use the same specular conversation as Cycles principled specular?
If you use this shader and specular settings then the answer is no.
i guess you have set the specular weight ,in your Arnold settings,in the first example post?
If i am not wrong,then the Specular weight, is how much of the reflection is mixed in. IE 0.01 are 1 % overall reflection.
This is not the same as the principled specular works,look the principled specular formula in my first post.
To simulate the behavior of the principled specular with Arnold,you have to set the weight to 1,the color to white (1,1,1) and roughness 0.
Now you have to decrease just the IOR in the Arnold specular settings.
But keep in mid that the principled uses the specular conversation.you can put in the same IOR with a little math.
here a quick IOR to specular node build.notice that IOR lower than 1 does not work.