The JH-13's do sound very good out of the iPhone/iPod classic, but they improve a load by using an amp. I dont want to try to quantify the number with a percentage better though. But the bass gets deeper and more impactful, and they open up quite a bit as well. Also once you have an amp, you can use a better source. Without a seperate amp i would not be able to use mine with my dac19 at home.
On the issue of cables, i bought the TWag because i needed it to go balanced with the protector, you can't do that with the stock cable, and also because i think it looks awesome
i have never compared it to the stock cable, because i never listened to the stock cable, my TWag got to my house before the jh-13's so there was no reason to.