I just received my Iphone 5s yesterday night , until now Iphone 4 S is the best from all iPhone series I have .
Out the box Iphone 5 S sound quality is very good .
I haven't done briefly comparison between these two
As apple fan boy I bought every time Iphone came out the new model Except iPhone 5 , because IPhone 5 sound Quality was below my 4 G and 4 S.
Here is the answer for the volume between Iphone 4 S and 5 S:
Like you see in my picture , I use the same music file
At the Same volume level these two phone have almost the same loud with the same hp out
iPhone 4 s only slightly Lauder not that much
This is the reason I bought iPhone 5 s , because of the sq and volume
Note : I haven't tested the speaker out , how loud can produce the iPhone 5s , because I need to buy screen protector first
And I just play last than 5 hours , about the SQ comparison I will do later after burn in